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A322802
Number of compositions (ordered partitions) of n into centered hexagonal numbers (A003215).
3
1, 1, 1, 1, 1, 1, 1, 2, 3, 4, 5, 6, 7, 8, 10, 13, 17, 22, 28, 36, 45, 56, 70, 88, 111, 140, 178, 226, 286, 361, 455, 573, 721, 909, 1148, 1451, 1834, 2318, 2928, 3695, 4661, 5880, 7420, 9366, 11826, 14935, 18860, 23812, 30059, 37941, 47888, 60445, 76302, 96327
OFFSET
0,8
FORMULA
G.f.: 1/(1 - Sum_{k>=0} x^(3*k*(k+1)+1)).
MAPLE
h:= proc(n) option remember; `if`(n<0, 0, (t->
`if`(3*t*(t+1)+1>n, t-1, t))(1+h(n-1)))
end:
a:= proc(n) option remember; `if`(n=0, 1,
add(a(n-(3*i*(i+1)+1)), i=0..h(n)))
end:
seq(a(n), n=0..60); # Alois P. Heinz, Dec 28 2018
MATHEMATICA
nmax = 53; CoefficientList[Series[1/(1 - Sum[x^(3 k (k + 1) + 1), {k, 0, nmax}]), {x, 0, nmax}], x]
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Dec 26 2018
STATUS
approved