A164420 Number of binary strings of length n with no substrings equal to 0000, 0010, or 0111.

1, 2, 4, 8, 13, 21, 33, 52, 81, 125, 193, 297, 457, 702, 1078, 1655, 2540, 3898, 5981, 9177, 14080, 21602, 33142, 50846, 78007, 119676, 183603, 281677, 432138, 662969, 1017100, 1560393, 2393890, 3672606, 5634358, 8643995, 13261253, 20344855, 31212218, 47884467

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 (1,1,0,0,0,-1).

Formula

G.f.: (x+1)*(x^3+x^2+1)/((x-1)*(x^5+x^4+x^3+x^2-1)). - R. J. Mathar, Dec 01 2011

Mathematica

CoefficientList[Series[(x + 1) (x^3 + x^2 + 1)/((x - 1) (x^5 + x^4 + x^3 + x^2 - 1)), {x, 0, 39}], x] (* Michael De Vlieger, Oct 11 2017 *)

Crossrefs

Sequence in context: A241691 A164429 A073336 * A164457 A164419 A164480

Adjacent sequences: A164417 A164418 A164419 * A164421 A164422 A164423

Keyword

nonn,easy

Author

R. H. Hardin, Aug 14 2009

Extensions

Edited by Alois P. Heinz, Oct 09 2017

Status

approved