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Number of binary strings of length n+7 such that the smallest number whose binary representation is not visible in the string is 9.
2

%I #8 Aug 20 2015 23:22:13

%S 0,2,12,52,168,461,1133,2612,5759,12309,25666,52509,105803,210655,

%T 415349,812461,1578752,3050921,5868562,11244267,21472441,40887802,

%U 77668032,147222550,278556477,526215993,992694708,1870443330,3520594166,6620431857,12439538938

%N Number of binary strings of length n+7 such that the smallest number whose binary representation is not visible in the string is 9.

%H Alois P. Heinz, <a href="/A261474/b261474.txt">Table of n, a(n) for n = 0..1000</a>

%F G.f.: (x^28 +x^27 -3*x^26 +4*x^25 +12*x^24 -20*x^23 -8*x^22 +55*x^21 -37*x^20 -85*x^19 +123*x^18 +21*x^17 -208*x^16 +117*x^15 +166*x^14 -227*x^13 -17*x^12 +235*x^11 -108*x^10 -122*x^9 +134*x^8 +8*x^7 -86*x^6 +31*x^5 +21*x^4 -18*x^3 +12*x^2 -8*x+2)*x / ((x+1) *(x^2-x+1) *(x^2+x-1) *(x^4-x^3+2*x-1) *(x^5+x^4+x-1) *(x^5+x^2+x-1) *(x^4-x^3+x^2+x-1) *(x^3+x^2-1) *(x^4+x-1) *(x-1)^3).

%F a(n) = A261019(n+7,9).

%Y Column k=9 of A261019.

%K nonn,easy

%O 0,2

%A _Alois P. Heinz_, Aug 20 2015