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.
0, 2, 24, 130, 471, 1401, 3734, 9258, 21826, 49561, 109261, 235327, 497495, 1035744, 2129126, 4330524, 8729070, 17460382, 34695315, 68549561, 134764551, 263788114, 514366212, 999590406, 1936741832, 3742534848, 7214885826, 13879427752, 26649404779, 51081190435
Offset: 0
Links
- Alois P. Heinz, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, 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).
Crossrefs
Column k=10 of A261019.
Formula
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).
a(n) = A261019(n+10,10).