OFFSET
0,2
COMMENTS
Number of ways to write n as an ordered sum of 5 tetrahedral (or triangular pyramidal) numbers (A000292).
a(n) > 0 for all n ("Pollock's Conjecture").
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..10000
Ilya Gutkovskiy, Extended graphical example
Eric Weisstein's World of Mathematics, Pollock's Conjecture
Eric Weisstein's World of Mathematics, Tetrahedral Number
FORMULA
G.f.: (Sum_{k>=0} x^(k*(k+1)*(k+2)/6))^5.
EXAMPLE
a(4) = 10 because we have:
[4, 0, 0, 0, 0]
[0, 4, 0, 0, 0]
[0, 0, 4, 0, 0]
[0, 0, 0, 4, 0]
[0, 0, 0, 0, 4]
[1, 1, 1, 1, 0]
[1, 1, 1, 0, 1]
[1, 1, 0, 1, 1]
[1, 0, 1, 1, 1]
[0, 1, 1, 1, 1]
MATHEMATICA
nmax = 75; CoefficientList[Series[(Sum[x^(k (k + 1) (k + 2)/6), {k, 0, nmax}])^5, {x, 0, nmax}], x]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Feb 07 2017
STATUS
approved