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A282350 Expansion of (Sum_{k>=0} x^(k*(5*k^2-5*k+2)/2))^15. 1
1, 15, 105, 455, 1365, 3003, 5005, 6435, 6435, 5005, 3003, 1365, 470, 315, 1380, 5461, 15015, 30030, 45045, 51480, 45045, 30030, 15015, 5460, 1470, 1575, 8205, 30030, 75075, 135135, 180180, 180180, 135135, 75075, 30030, 8190, 1820, 5565, 30030, 100100, 225225, 360360, 420420, 360360, 225225, 100100, 30030, 5460 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Number of ways to write n as an ordered sum of 15 icosahedral numbers (A006564).

Pollock conjectured that every number is the sum of at most 5 tetrahedral numbers and that every number is the sum of at most 7 octahedral numbers.

Conjecture: a(n) > 0 for all n >= 0.

Extended conjecture: every number is the sum of at most 15 icosahedral numbers.

LINKS

Table of n, a(n) for n=0..47.

Ilya Gutkovskiy, Extended graphical example

FORMULA

G.f.: (Sum_{k>=0} x^(k*(5*k^2-5*k+2)/2))^15.

MATHEMATICA

nmax = 47; CoefficientList[Series[Sum[x^(k (5 k^2 - 5 k + 2)/2), {k, 0, nmax}]^15, {x, 0, nmax}], x]

CROSSREFS

Cf. A006564, A282172, A282349.

Sequence in context: A296912 A202288 A010931 * A076767 A022610 A006857

Adjacent sequences:  A282347 A282348 A282349 * A282351 A282352 A282353

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Feb 12 2017

STATUS

approved

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Last modified October 17 22:48 EDT 2018. Contains 316297 sequences. (Running on oeis4.)