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A282248 Expansion of (Sum_{k>=0} x^(k*(5*k-3)/2))^7. 3
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 (list; graph; refs; listen; history; text; internal format)
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 A045849 A031008

Adjacent sequences:  A282245 A282246 A282247 * A282249 A282250 A282251

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Feb 09 2017

STATUS

approved

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Last modified August 21 06:54 EDT 2019. Contains 326162 sequences. (Running on oeis4.)