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 A282582 Number of compositions (ordered partitions) of n into tetrahedral (or triangular pyramidal) numbers (A000292). 7
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 LINKS Indranil Ghosh, Table of n, a(n) for n = 0..100 Eric Weisstein's World of Mathematics, Tetrahedral Number 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 Cf. A000292, A023361, A068980, A279278, A282172. Sequence in context: A107586 A206737 A275174 * A282502 A212463 A130080 Adjacent sequences:  A282579 A282580 A282581 * A282583 A282584 A282585 KEYWORD nonn AUTHOR Ilya Gutkovskiy, Feb 19 2017 STATUS approved

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Last modified January 19 21:47 EST 2020. Contains 331066 sequences. (Running on oeis4.)