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Number of length-n binary vectors beginning with 0, ending with 1, and avoiding 7 consecutive 0's and 7 consecutive 1's.
3

%I #14 Mar 26 2017 11:43:32

%S 1,0,1,2,4,8,16,32,62,124,246,488,968,1920,3809,7554,14985,29724,

%T 58960,116952,231984,460160,912764,1810544,3591364,7123768,14130584,

%U 28029184,55598209,110283652,218756761,433922158,860720548,1707310512,3386591840,6717585472

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

%H Alois P. Heinz, <a href="/A283837/b283837.txt">Table of n, a(n) for n = 0..1000</a>

%H Stefano Bilotta, <a href="http://arxiv.org/abs/1605.03785">Variable-length Non-overlapping Codes</a>, arXiv preprint arXiv:1605.03785 [cs.IT], 2016 [See Table 2].

%F 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

%t 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 *)

%o (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

%K nonn,easy

%O 0,4

%A _N. J. A. Sloane_, Mar 25 2017

%E More terms from _Alois P. Heinz_, Mar 25 2017