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A120118
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a(n) is the number of binary strings of length n such that no subsequence of length 5 or less contains 3 or more ones.
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5
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1, 2, 4, 7, 11, 16, 26, 43, 71, 116, 186, 300, 487, 792, 1287, 2087, 3382, 5484, 8898, 14438, 23423, 37993, 61625, 99965, 162165, 263065, 426736, 692229, 1122903, 1821538, 2954849, 4793266, 7775472, 12613097, 20460538, 33190414, 53840404
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OFFSET
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0,2
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LINKS
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Table of n, a(n) for n=0..36.
Kees Immink, Kui Cai, Properties and construtions of energy-harvesting sliding-window constrained codes, IEEE Comm. Lett., May 2020
Index entries for linear recurrences with constant coefficients, signature (1,0,1,0,2,0,0,-1,0,-1).
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FORMULA
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a(n) = a(n-1) + a(n-3) + 2a(n-5) - a(n-8) - a(n-10).
G.f.: 1-x*(1+x+x^2)*(x^7+x^5+x^4-x^3-x^2-2) / ( 1-x-x^3-2*x^5+x^8+x^10 ). - R. J. Mathar, Nov 28 2011
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EXAMPLE
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This sequence is similar to A118647 - where no subsequence of length 4 contains 3 ones. It is obvious that the first 4 terms of these two sequences are the same. There are only 3 sequences of length 5 that contain 3 ones such that no subsequence of length 4 contains 3 ones: 10101, 11001, 10011. Hence the fifth term for this sequence is 3 less than the corresponding term of A118647.
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MATHEMATICA
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LinearRecurrence[{1, 0, 1, 0, 2, 0, 0, -1, 0, -1}, {2, 4, 7, 11, 16, 26, 43, 71, 116, 186}, 50] (* Harvey P. Dale, Nov 27 2013 *)
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CROSSREFS
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Cf. A118647, A133523, A133551, A334251, A335247.
Sequence in context: A099385 A331387 A237821 * A108895 A146929 A146921
Adjacent sequences: A120115 A120116 A120117 * A120119 A120120 A120121
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KEYWORD
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nonn,easy
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AUTHOR
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Tanya Khovanova, Aug 15 2006, Oct 11 2006
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STATUS
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approved
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