A184714 Number of words of numbers x(1), ..., x(n), in 0..3 such that Sum_{i=1..n} i*x(i)^3 = 27*n.

1, 1, 2, 2, 7, 19, 39, 120, 411, 1310, 3862, 11059, 31849, 89615, 247305, 674579, 1812940, 4806211, 12576930, 32509641, 83052304, 209808493, 524424707, 1297623584, 3179903180, 7721053410, 18582920108, 44349211490, 104989527861, 246624184465, 575024282279

Offset

1,3

Comments

Coefficient of x^(27*n) in Product_{i=1..n} (1 + x^i + x^(8*i) + x^(27*i)). - Robert Israel, Jul 03 2018

Links

R. H. Hardin, Table of n, a(n) for n = 1..102

Example

All solutions for n=5:
  0    0    3    2    1    1    2
  0    3    0    2    1    2    1
  0    3    0    1    2    3    3
  0    0    3    3    3    2    1
  3    0    0    0    0    1    2

Maple

F:= proc(n, s) option remember; if n = 1 or s < 0 then 0 else add(procname(n-1, s-n*j^3), j=0..3) fi end proc:
F(1, 0):= 1: F(1, 1):= 1: F(1, 8):= 1: F(1, 27):= 1:
seq(F(n, n*27), n=1..50); # Robert Israel, Jul 03 2018

Mathematica

F[n_, s_] := F[n, s] = If[n == 1 || s < 0, 0, Sum[F[n-1, s-n*j^3], {j, 0, 3}]]; F[1, 0] = 1; F[1, 1] = 1; F[1, 8] = 1; F[1, 27] = 1;
Table[F[n, 27 n], {n, 1, 50}] (* Jean-François Alcover, May 23 2023, after Robert Israel *)

Crossrefs

Column 3 of A184720.

Sequence in context: A338415 A243022 A049955 * A156464 A156520 A307426

Adjacent sequences: A184711 A184712 A184713 * A184715 A184716 A184717

Keyword

nonn

Author

R. H. Hardin, Jan 20 2011

Status

approved