A164431 Number of binary strings of length n with no substrings equal to 0000, 0011 or 1101.

1, 2, 4, 8, 13, 21, 34, 54, 86, 139, 225, 364, 590, 956, 1547, 2503, 4050, 6552, 10600, 17151, 27751, 44902, 72654, 117558, 190213, 307771, 497984, 805754, 1303736, 2109489, 3413225, 5522714, 8935940, 14458656, 23394597, 37853253, 61247850, 99101102

Offset

0,2

Links

Alois P. Heinz, Table of n, a(n) for n = 0..2000 (terms n = 4..500 from R. H. Hardin)

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

Formula

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

Mathematica

LinearRecurrence[{2, -1, 1, -1, 0, 1}, {13, 21, 34, 54, 86, 139}, 40] (* Harvey P. Dale, May 19 2016 *)

Crossrefs

Sequence in context: A164420 A164457 A164419 * A164480 A134035 A351620

Adjacent sequences: A164428 A164429 A164430 * A164432 A164433 A164434

Keyword

nonn,easy

Author

R. H. Hardin, Aug 14 2009

Extensions

a(0)-a(3) prepended by Alois P. Heinz, Apr 03 2024

Status

approved