OFFSET
0,2
COMMENTS
Number of ways to write n as an ordered sum of 7 heptagonal numbers (A000566).
a(n) > 0 for all n >= 0.
Every number is the sum of at most 7 heptagonal numbers.
Every number is the sum of at most k k-gonal numbers (Fermat's polygonal number theorem).
LINKS
Ilya Gutkovskiy, Extended graphical example
Eric Weisstein's World of Mathematics, Heptagonal Number
FORMULA
G.f.: (Sum_{k>=0} x^(k*(5*k-3)/2))^7.
EXAMPLE
a(7) = 8 because we have
[7, 0, 0, 0, 0, 0, 0]
[0, 7, 0, 0, 0, 0, 0]
[0, 0, 7, 0, 0, 0, 0]
[0, 0, 0, 7, 0, 0, 0]
[0, 0, 0, 0, 7, 0, 0]
[0, 0, 0, 0, 0, 7, 0]
[0, 0, 0, 0, 0, 0, 7]
[1, 1, 1, 1, 1, 1, 1]
MATHEMATICA
nmax = 67; CoefficientList[Series[Sum[x^(k (5 k - 3)/2), {k, 0, nmax}]^7, {x, 0, nmax}], x]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Feb 09 2017
STATUS
approved