A309295 (1/3) times the sum of the elements of all subsets of [n] whose sum is divisible by three.

0, 0, 1, 4, 9, 30, 84, 202, 528, 1320, 3144, 7568, 17888, 41472, 95760, 218880, 495344, 1114656, 2491584, 5534688, 12234880, 26916736, 58954752, 128629248, 279628800, 605847808, 1308632832, 2818593792, 6054720768, 12974405120, 27738383360, 59175129600

Offset: 0

Author

Alois P. Heinz, Jul 21 2019

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 (6,-12,14,-36,72,-60,72,-144,104,-48,96,-64).

Crossrefs

Column k=3 of A309280.

Programs

Mathematica

CoefficientList[Series[-x^2(8x^8-4x^5+8x^4-10x^3+3x^2+2x-1)/((2x-1)^3(2x^3-1)^3),{x,0,40}],x] (* or *) LinearRecurrence[{6,-12,14,-36,72,-60,72,-144,104,-48,96,-64},{0,0,1,4,9,30,84,202,528,1320,3144,7568},40] (* Harvey P. Dale, Mar 17 2023 *)

Formula

G.f.: -x^2*(8*x^8-4*x^5+8*x^4-10*x^3+3*x^2+2*x-1)/((2*x-1)^3*(2*x^3-1)^3).