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

0,4

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).

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).

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 *)

Crossrefs

Column k=3 of A309280.

Sequence in context: A297960 A295910 A086688 * A151270 A149113 A149114

Adjacent sequences: A309292 A309293 A309294 * A309296 A309297 A309298

Keyword

nonn,easy

Author

Alois P. Heinz, Jul 21 2019

Status

approved