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

0,2

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

Table of n, a(n) for n=0..67.

Ilya Gutkovskiy, Extended graphical example

Eric Weisstein's World of Mathematics, Heptagonal Number

Index to sequences related to polygonal numbers

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

Cf. A000566, A045849, A213523, A226252.

Sequence in context: A087111 A173676 A131893 * A282349 A356454 A045849

Adjacent sequences: A282245 A282246 A282247 * A282249 A282250 A282251

Keyword

nonn

Author

Ilya Gutkovskiy, Feb 09 2017

Status

approved