A164416 Number of binary strings of length n with no substrings equal to 0000 0001 or 1111.

13, 23, 40, 69, 120, 208, 361, 626, 1086, 1884, 3268, 5669, 9834, 17059, 29592, 51333, 89047, 154469, 267956, 464821, 806321, 1398718, 2426344, 4208958, 7301243, 12665403, 21970565, 38112149, 66112815, 114685328, 198943646, 345105821

Offset

4,1

Links

R. H. Hardin, Table of n, a(n) for n = 4..500

Index entries for linear recurrences with constant coefficients, signature (0,1,2,2,1).

Formula

G.f.: -x^4*(13+23*x+27*x^2+20*x^3+8*x^4) / ( -1+x^2+2*x^3+2*x^4+x^5 ). - R. J. Mathar, Nov 30 2011

Prog

(PARI) a(n)=([0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1; 1, 2, 2, 1, 0]^(n-4)*[13; 23; 40; 69; 120])[1, 1] \\ Charles R Greathouse IV, Jun 05 2026

Crossrefs

Sequence in context: A070219 A046119 A374102 * A164491 A164434 A164494

Adjacent sequences: A164413 A164414 A164415 * A164417 A164418 A164419

Keyword

nonn,easy

Author

R. H. Hardin, Aug 14 2009

Status

approved