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Number of binary strings of length n+5 such that the smallest number whose binary representation is not visible in the string is 7.
2

%I #6 Aug 20 2015 15:42:04

%S 0,2,9,31,79,185,408,864,1771,3555,7021,13696,26453,50700,96565,

%T 182983,345269,649188,1217000,2275699,4246229,7908427,14705711,

%U 27307682,50648414,93841900,173714334,321316013,593922885,1097150252,2025690002,3738341466,6896182121

%N Number of binary strings of length n+5 such that the smallest number whose binary representation is not visible in the string is 7.

%H Alois P. Heinz, <a href="/A261443/b261443.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_16">Index entries for linear recurrences with constant coefficients</a>, signature (4,-3,-3,-1,3,7,2,-4,-10,-3,3,7,3,-1,-2,-1).

%F a(n) = A261019(n+5,7).

%F G.f.: -(x^12+3*x^11+3*x^10-8*x^8-13*x^7-14*x^6-x^5+9*x^4+12*x^3-x^2-x-2)*x / ((x+1)*(x^2+1)*(x^2+x-1)*(x^3+x^2-1)*(x^3+x^2+x-1)*(x^3+x-1)*(x-1)^2). - _Alois P. Heinz_, Aug 19 2015

%o (Haskell)

%o a261443 n = a261019' (n + 5) 7

%Y Column k=7 of A261019.

%K nonn,easy

%O 0,2

%A _Reinhard Zumkeller_, Aug 18 2015

%E More terms from _Alois P. Heinz_, Aug 19 2015