A282248 Expansion of (Sum_{k>=0} x^(k*(5*k-3)/2))^7.

1, 7, 21, 35, 35, 21, 7, 8, 42, 105, 140, 105, 42, 7, 21, 105, 210, 210, 112, 63, 105, 175, 245, 252, 147, 77, 210, 420, 455, 315, 147, 35, 105, 420, 637, 483, 273, 266, 315, 392, 532, 483, 357, 532, 840, 840, 567, 315, 210, 421, 840, 1050, 777, 462, 497, 707, 882, 917, 735, 525, 889, 1407, 1407, 1050, 770, 525, 630, 1302

Offset: 0

Author

Ilya Gutkovskiy, Feb 09 2017

Keywords

• nonn

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).

Examples

			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]
		

Links

• Ilya Gutkovskiy, Extended graphical example
• Eric Weisstein's World of Mathematics, Heptagonal Number
• Index to sequences related to polygonal numbers

Crossrefs

Cf. A000566, A045849, A213523, A226252.

Programs

Mathematica

nmax = 67; CoefficientList[Series[Sum[x^(k (5 k - 3)/2), {k, 0, nmax}]^7, {x, 0, nmax}], x]

Formula

G.f.: (Sum_{k>=0} x^(k*(5*k-3)/2))^7.