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URL: https://oeis.org/A322801

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A322801
Number of compositions (ordered partitions) of n into centered pentagonal numbers (A005891).
3
1, 1, 1, 1, 1, 1, 2, 3, 4, 5, 6, 7, 9, 12, 16, 21, 28, 36, 46, 59, 76, 98, 128, 167, 217, 281, 363, 468, 605, 784, 1017, 1320, 1712, 2217, 2869, 3713, 4807, 6227, 8070, 10458, 13549, 17549, 22726, 29430, 38117, 49375, 63962, 82859, 107333, 139026, 180071
OFFSET
0,7
FORMULA
G.f.: 1/(1 - Sum_{k>=0} x^(5*k*(k+1)/2+1)).
MAPLE
h:= proc(n) option remember; `if`(n<0, 0, (t->
`if`(((t+1)*5*t+2)/2>n, t-1, t))(1+h(n-1)))
end:
a:= proc(n) option remember; `if`(n=0, 1,
add(a(n-((i+1)*5*i+2)/2), i=0..h(n)))
end:
seq(a(n), n=0..60); # Alois P. Heinz, Dec 28 2018
MATHEMATICA
nmax = 50; CoefficientList[Series[1/(1 - Sum[x^(5 k (k + 1)/2 + 1), {k, 0, nmax}]), {x, 0, nmax}], x]
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Dec 26 2018
STATUS
approved