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A322856
Number of compositions (ordered partitions) of n into octagonal pyramidal numbers (A002414).
3
1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 15, 19, 24, 30, 37, 45, 54, 64, 76, 91, 110, 135, 166, 204, 250, 305, 370, 447, 539, 650, 787, 956, 1164, 1419, 1730, 2107, 2562, 3110, 3770, 4569, 5540, 6723, 8166, 9926, 12070, 14677, 17841, 21675
OFFSET
0,10
FORMULA
G.f.: 1/(1 - Sum_{k>=1} x^(k*(k+1)*(2*k-1)/2)).
MATHEMATICA
nmax = 56; CoefficientList[Series[1/(1 - Sum[x^(k (k + 1) (2 k - 1)/2), {k, 1, nmax}]), {x, 0, nmax}], x]
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Dec 29 2018
STATUS
approved