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A282582
Number of compositions (ordered partitions) of n into tetrahedral (or triangular pyramidal) numbers (A000292).
16
1, 1, 1, 1, 2, 3, 4, 5, 7, 10, 15, 21, 29, 40, 57, 81, 114, 159, 223, 314, 444, 625, 878, 1233, 1736, 2445, 3441, 4838, 6804, 9573, 13473, 18957, 26668, 37514, 52780, 74264, 104488, 147000, 206808, 290961, 409369, 575955, 810314, 1140029, 1603924, 2256603, 3174867, 4466763, 6284339, 8841533, 12439323
OFFSET
0,5
FORMULA
G.f.: 1/(1 - Sum_{k>=1} x^(k*(k+1)*(k+2)/6)).
EXAMPLE
a(8) = 7 because we have [4, 4], [4, 1, 1, 1, 1], [1, 4, 1, 1, 1], [1, 1, 4, 1, 1], [1, 1, 1, 4, 1], [1, 1, 1, 1, 4] and [1, 1, 1, 1, 1, 1, 1, 1].
MATHEMATICA
nmax = 50; CoefficientList[Series[1/(1 - Sum[x^(k (k + 1) (k + 2)/6), {k, 1, nmax}]), {x, 0, nmax}], x]
PROG
(PARI) Vec(1/(1 - sum(k=1, 50, x^(k*(k + 1)*(k + 2)/6)) + O(x^51))) \\ Indranil Ghosh, Mar 15 2017
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Feb 19 2017
STATUS
approved