A164478 Number of binary strings of length n with no substrings equal to 0001 0110 or 1010.

13, 20, 31, 49, 78, 123, 193, 303, 476, 748, 1175, 1845, 2897, 4549, 7143, 11216, 17611, 27652, 43418, 68173, 107042, 168072, 263898, 414359, 650605, 1021546, 1603978, 2518482, 3954388, 6208972, 9749001, 15307368, 24034823, 37738213, 59254554

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 (2,-1,1,-1,1,-1).

Formula

G.f.: -x^4*(-13+6*x-4*x^2+6*x^3-4*x^4+8*x^5) / ( (x-1)*(x^5+x^3+x-1) ). - R. J. Mathar, Jan 19 2011

Mathematica

LinearRecurrence[{2, -1, 1, -1, 1, -1}, {13, 20, 31, 49, 78, 123}, 40] (* Harvey P. Dale, Sep 22 2020 *)

Crossrefs

Sequence in context: A164484 A164502 A164474 * A164463 A164470 A164469

Adjacent sequences: A164475 A164476 A164477 * A164479 A164480 A164481

Keyword

nonn,easy

Author

R. H. Hardin, Aug 14 2009

Status

approved