A283837 Number of length-n binary vectors beginning with 0, ending with 1, and avoiding 7 consecutive 0's and 7 consecutive 1's.

1, 0, 1, 2, 4, 8, 16, 32, 62, 124, 246, 488, 968, 1920, 3809, 7554, 14985, 29724, 58960, 116952, 231984, 460160, 912764, 1810544, 3591364, 7123768, 14130584, 28029184, 55598209, 110283652, 218756761, 433922158, 860720548, 1707310512, 3386591840, 6717585472

Offset

0,4

Links

Alois P. Heinz, Table of n, a(n) for n = 0..1000

Stefano Bilotta, Variable-length Non-overlapping Codes, arXiv preprint arXiv:1605.03785 [cs.IT], 2016 [See Table 2].

Formula

G.f.: -1/((x^6+x^5+x^4+x^3+x^2+x+1)*(x^6+x^5+x^4+x^3+x^2+x-1)). - Alois P. Heinz, Mar 25 2017

Mathematica

CoefficientList[Series[-1/((x^6 + x^5 + x^4 + x^3 + x^2 + x + 1)*(x^6 + x^5 + x^4 + x^3 + x^2 + x - 1)), {x, 0, 50}], x] (* Indranil Ghosh, Mar 26 2017 *)

Prog

(PARI) Vec(-1/((x^6 + x^5 + x^4 + x^3 + x^2 + x + 1)*(x^6 + x^5 + x^4 + x^3 + x^2 + x - 1)) + O(x^50)) \\ Indranil Ghosh, Mar 26 2017

Crossrefs

Sequence in context: A027560 A135493 A216241 * A111663 A054043 A052396

Adjacent sequences: A283834 A283835 A283836 * A283838 A283839 A283840

Keyword

nonn,easy

Author

N. J. A. Sloane, Mar 25 2017

Extensions

More terms from Alois P. Heinz, Mar 25 2017

Status

approved