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A282582 Number of compositions (ordered partitions) of n into tetrahedral (or triangular pyramidal) numbers (A000292).

%I A282582 #8 Feb 16 2025 08:33:41
%S A282582 1,1,1,1,2,3,4,5,7,10,15,21,29,40,57,81,114,159,223,314,444,625,878,
%T A282582 1233,1736,2445,3441,4838,6804,9573,13473,18957,26668,37514,52780,
%U A282582 74264,104488,147000,206808,290961,409369,575955,810314,1140029,1603924,2256603,3174867,4466763,6284339,8841533,12439323
%N A282582 Number of compositions (ordered partitions) of n into tetrahedral (or triangular pyramidal) numbers (A000292).
%H A282582 Indranil Ghosh, <a href="/A282582/b282582.txt">Table of n, a(n) for n = 0..100</a>
%H A282582 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/TetrahedralNumber.html">Tetrahedral Number</a>
%H A282582 <a href="/index/Ps#pyramidal_numbers">Index to sequences related to pyramidal numbers</a>
%H A282582 <a href="/index/Com#comp">Index entries for sequences related to compositions</a>
%F A282582 G.f.: 1/(1 - Sum_{k>=1} x^(k*(k+1)*(k+2)/6)).
%e A282582 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].
%t A282582 nmax = 50; CoefficientList[Series[1/(1 - Sum[x^(k (k + 1) (k + 2)/6), {k, 1, nmax}]), {x, 0, nmax}], x]
%o A282582 (PARI) Vec(1/(1 - sum(k=1, 50, x^(k*(k + 1)*(k + 2)/6)) + O(x^51))) \\ _Indranil Ghosh_, Mar 15 2017
%Y A282582 Cf. A000292, A023361, A068980, A279278, A282172.
%K A282582 nonn
%O A282582 0,5
%A A282582 _Ilya Gutkovskiy_, Feb 19 2017