A309301 (1/9) times the sum of the elements of all subsets of [n] whose sum is divisible by nine.
0, 0, 0, 0, 1, 3, 9, 23, 60, 150, 354, 843, 1983, 4608, 10638, 24318, 55043, 123862, 276868, 614996, 1359446, 2990726, 6550528, 14292132, 31069860, 67316446, 145403700, 313177200, 672746880, 1441600632, 3082042512, 6575014400, 13998418584, 29746639512
Offset: 0
Links
- Alois P. Heinz, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (6, -12, 14, -36, 72, -60, 72, -144, 110, -84, 168, -148, 216, -432, 360, -432, 864, -636, 360, -720, 552, -432, 864, -720, 864, -1728, 1256, -624, 1248, -880, 288, -576, 480, -576, 1152, -832, 384, -768, 512).
Crossrefs
Column k=9 of A309280.
Formula
G.f.: -x^4*(64*x^33-160*x^30+32*x^29+80*x^28+216*x^27+96*x^26 -312*x^25 -160*x^24 -200*x^23 +376*x^22+40*x^21 -4*x^20+164*x^19-48*x^18 +60*x^17 -516*x^16 +114*x^15+4*x^14+340*x^13-79*x^12-30*x^11-78*x^10 +4*x^9 +45*x^8 -33*x^7+20*x^6-24*x^5+24*x^4-9*x^3+3*x^2 -3*x+1) / ((2*x-1)^3 *(2*x^3-1)^3 *(2*x^9-1)^3).