

A120118


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.


5



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

0,2


LINKS

Table of n, a(n) for n=0..36.
Kees Immink, Kui Cai, Properties and construtions of energyharvesting slidingwindow 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).


FORMULA

a(n) = a(n1) + a(n3) + 2a(n5)  a(n8)  a(n10).
G.f.: 1x*(1+x+x^2)*(x^7+x^5+x^4x^3x^22) / ( 1xx^32*x^5+x^8+x^10 ).  R. J. Mathar, Nov 28 2011


EXAMPLE

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.


MATHEMATICA

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 *)


CROSSREFS

Cf. A118647, A133523, A133551, A334251, A335247.
Sequence in context: A099385 A331387 A237821 * A108895 A146929 A146921
Adjacent sequences: A120115 A120116 A120117 * A120119 A120120 A120121


KEYWORD

nonn,easy


AUTHOR

Tanya Khovanova, Aug 15 2006, Oct 11 2006


STATUS

approved



