This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A261474 #12 Jul 23 2025 13:33:51
%S A261474 0,2,12,52,168,461,1133,2612,5759,12309,25666,52509,105803,210655,
%T A261474 415349,812461,1578752,3050921,5868562,11244267,21472441,40887802,
%U A261474 77668032,147222550,278556477,526215993,992694708,1870443330,3520594166,6620431857,12439538938
%N A261474 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 A261474 Alois P. Heinz, <a href="/A261474/b261474.txt">Table of n, a(n) for n = 0..1000</a>
%H A261474 <a href="/index/Rec#order_33">Index entries for linear recurrences with constant coefficients</a>, signature (10, -40, 73, -18, -184, 344, -119, -447, 680, -55, -833, 792, 294, -1086, 538, 618, -896, 88, 638, -452, -176, 395, -115, -160, 141, 7, -64, 26, 12, -13, 2, 2, -1).
%F A261474 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 A261474 a(n) = A261019(n+7,9).
%t A261474 CoefficientList[Series[(x^28+x^27-3x^26+4x^25+12x^24-20x^23-8x^22+55x^21-37x^20-85x^19+123x^18+21x^17-208x^16+117x^15+166x^14-227x^13-17x^12+235x^11-108x^10-122x^9+134x^8+8x^7-86x^6+31x^5+21x^4-18x^3+12x^2-8x+2)x/((x+1)(x^2-x+1)(x^2+x-1)(x^4-x^3+2x-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),{x,0,30}],x] (* or *) LinearRecurrence[{10,-40,73,-18,-184,344,-119,-447,680,-55,-833,792,294,-1086,538,618,-896,88,638,-452,-176,395,-115,-160,141,7,-64,26,12,-13,2,2,-1},{0,2,12,52,168,461,1133,2612,5759,12309,25666,52509,105803,210655,415349,812461,1578752,3050921,5868562,11244267,21472441,40887802,77668032,147222550,278556477,526215993,992694708,1870443330,3520594166,6620431857,12439538938,23356730756,43827457565},40] (* _Harvey P. Dale_, Jul 23 2025 *)
%Y A261474 Column k=9 of A261019.
%K A261474 nonn,easy
%O A261474 0,2
%A A261474 _Alois P. Heinz_, Aug 20 2015