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.

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

Offset: 0

Author

Alois P. Heinz, Aug 20 2015

Keywords

• nonn
• easy

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, 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).

Crossrefs

Column k=9 of A261019.

Programs

Mathematica

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 *)

Formula

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).

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