A164480 Number of binary strings of length n with no substrings equal to 0001, 0110 or 1100.

1, 2, 4, 8, 13, 21, 34, 55, 88, 142, 229, 370, 598, 967, 1564, 2530, 4093, 6622, 10714, 17335, 28048, 45382, 73429, 118810, 192238, 311047, 503284, 814330, 1317613, 2131942, 3449554, 5581495, 9031048, 14612542, 23643589, 38256130, 61899718, 100155847

Offset

0,2

Links

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

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

Formula

From Colin Barker, Oct 27 2017: (Start)

G.f.: -(x^8+x^5+x^4-x^3-1)/((x-1)*(x^2+x-1)).

a(n) = 2*a(n-1) - a(n-3) for n>6.

(End)

a(n) = 3*Lucas(n-1) + 1 for n >= 6. - Greg Dresden, Oct 10 2020

Prog

(PARI) Vec(-(x^8+x^5+x^4-x^3-1)/((x-1)*(x^2+x-1)) + O(x^60)) \\ Colin Barker, Oct 27 2017

Crossrefs

Sequence in context: A164457 A164419 A164431 * A134035 A351620 A078157

Adjacent sequences: A164477 A164478 A164479 * A164481 A164482 A164483

Keyword

nonn,easy

Author

R. H. Hardin, Aug 14 2009

Extensions

Edited by Alois P. Heinz, Oct 27 2017

Status

approved