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A322340
Number of compositions (ordered partitions) of n into square pyramidal numbers (A000330).
6
1, 1, 1, 1, 1, 2, 3, 4, 5, 6, 8, 11, 15, 20, 27, 36, 48, 64, 85, 114, 153, 205, 274, 365, 487, 651, 871, 1165, 1557, 2080, 2780, 3716, 4967, 6639, 8873, 11860, 15853, 21189, 28320, 37850, 50589, 67618, 90379, 120799, 161456, 215797, 288430, 385512, 515269, 688699
OFFSET
0,6
FORMULA
G.f.: 1/(1 - Sum_{k>=1} x^(k*(k+1)*(2*k+1)/6)).
MAPLE
h:= proc(n) option remember; `if`(n<1, 0, (t->
`if`(t*(t+1)*(2*t+1)/6>n, t-1, t))(1+h(n-1)))
end:
a:= proc(n) option remember; `if`(n=0, 1,
add(a(n-i*(i+1)*(2*i+1)/6), i=1..h(n)))
end:
seq(a(n), n=0..60); # Alois P. Heinz, Dec 28 2018
MATHEMATICA
nmax = 49; CoefficientList[Series[1/(1 - Sum[x^(k (k + 1) (2 k + 1)/6), {k, 1, nmax}]), {x, 0, nmax}], x]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Dec 26 2018
STATUS
approved