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A261475 Number of binary strings of length n+10 such that the smallest number whose binary representation is not visible in the string is 10.

%I A261475 #10 Jul 24 2025 11:16:52
%S A261475 0,2,24,130,471,1401,3734,9258,21826,49561,109261,235327,497495,
%T A261475 1035744,2129126,4330524,8729070,17460382,34695315,68549561,134764551,
%U A261475 263788114,514366212,999590406,1936741832,3742534848,7214885826,13879427752,26649404779,51081190435
%N A261475 Number of binary strings of length n+10 such that the smallest number whose binary representation is not visible in the string is 10.
%H A261475 Alois P. Heinz, <a href="/A261475/b261475.txt">Table of n, a(n) for n = 0..1000</a>
%H A261475 <a href="/index/Rec#order_46">Index entries for linear recurrences with constant coefficients</a>, signature (13, -79, 310, -922, 2277, -4867, 9185, -15562, 23930, -33568, 43145, -50864, 54827, -53766, 47275, -36121, 22302, -8069, -4176, 12665, -17007, 17276, -14737, 10894, -6686, 3420, -1155, -139, 455, -614, 475, -364, 435, -326, 352, -269, 126, -75, -30, 42, -34, 30, -4, 1, 2, -2).
%F A261475 G.f.: -(4*x^38 +6*x^37 +7*x^36 +13*x^35 -40*x^34 -39*x^33 -144*x^32 -197*x^31 -142*x^30 -230*x^29 +157*x^28 +66*x^27 +679*x^26 +153*x^25 +850*x^24 -429*x^23 +260*x^22 -820*x^21 -624*x^20 +294*x^19 -1720*x^18 +3212*x^17 -4270*x^16 +6808*x^15 -7839*x^14 +8816*x^13 -8988*x^12 +7604*x^11 -6159*x^10 +4152*x^9 -2314*x^8 +1162*x^7 -331*x^6 -4*x^5 +48*x^4 -57*x^3 +24*x^2 +2*x-2)*x / ((x^2+1) *(x^2+x+1) *(x^2-x+1) *(x^2+x-1) *(2*x^3+x-1) *(x^3-x^2+2*x-1) *(x^4+x^3-1) *(x^4+x-1) *(x^5+x^3+x-1) *(x^5+x^4+x-1) *(x^4+2*x^3-1) *(x^4-2*x^3+x^2-2*x+1) *(x^3+x-1) *(x-1)^3).
%F A261475 a(n) = A261019(n+10,10).
%Y A261475 Column k=10 of A261019.
%K A261475 nonn,easy
%O A261475 0,2
%A A261475 _Alois P. Heinz_, Aug 20 2015