Problem 55990. Next Tribonacci Number

Created by Ben Placek

Solve Later

{"parts":[{"partUri":"/matlab/document.xml","contentType":"application/vnd.mathworks.matlab.code.document+xml","content":"<?xml version=\"1.0\" encoding=\"UTF-8\"?><w:document xmlns:w=\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\"><w:body><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>The \"Tribonacci\" sequence is an extension of the idea of the Fibonacci sequence:</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"true\"/></w:customXmlPr><w:r><w:t>T_0 = 0, T_1 = 1, T_2 = 1, \\dots, T_{n+1} = T_n + T_{n-1} + T_{n-2}</w:t></w:r></w:customXml></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>That is, each new term is the sum of the three previous terms.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>The first 10 Tribonacci numbers are: 0, 1, 1, 2, 4, 7, 13, 24, 44, 81.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>Given a value N, find the smallest Tribonacci number greater than N. You can assume N is a positive integer.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>For example, if N = 42, your function should return 44. If N = 17, your function should return 24.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t></w:t></w:r></w:p></w:body></w:document>","relationship":null}],"relationships":[{"relationshipType":"http://schemas.mathworks.com/matlab/code/2013/relationships/document","target":"/matlab/document.xml","relationshipId":"rId1"}]}

<div style = "text-align: start; line-height: 20px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: normal; text-decoration: none; white-space: normal; "><div style="block-size: 201px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; vertical-align: baseline; "><div style="block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; "><span style="">The "Tribonacci" sequence is an extension of the idea of the Fibonacci sequence:</span></span></div><div style="block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="vertical-align:-6px"><img src="data:image/png;base64,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" width="308.5" height="20" style="width: 308.5px; height: 20px;"></span></div><div style="block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; "><span style="">That is, each new term is the sum of the three previous terms.</span></span></div><div style="block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; "><span style="">The first 10 Tribonacci numbers are: 0, 1, 1, 2, 4, 7, 13, 24, 44, 81.</span></span></div><div style="block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; "><span style="">Given a value N, find the smallest Tribonacci number greater than N. You can assume N is a positive integer.</span></span></div><div style="block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; "><span style="">For example, if N = 42, your function should return 44. If N = 17, your function should return 24.</span></span></div><div style="block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; "><span style=""></span></span></div></div></div>

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Problem 55990. Next Tribonacci Number

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