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 A339420 Number of compositions (ordered partitions) of n into an even number of cubes. 2
 1, 0, 1, 0, 1, 0, 1, 0, 1, 2, 1, 4, 1, 6, 1, 8, 2, 10, 7, 12, 16, 14, 29, 16, 46, 22, 67, 40, 94, 78, 125, 144, 161, 246, 214, 394, 312, 602, 499, 878, 835, 1236, 1396, 1722, 2286, 2446, 3637, 3614, 5598, 5560, 8358, 8782, 12226, 14014, 17776, 22278, 26056, 34924 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,10 LINKS Alois P. Heinz, Table of n, a(n) for n = 0..5000 FORMULA G.f.: (1/2) * (1 / (1 - Sum_{k>=1} x^(k^3)) + 1 / Sum_{k>=0} x^(k^3)). a(n) = (A023358(n) + A323633(n)) / 2. a(n) = Sum_{k=0..n} A023358(k) * A323633(n-k). EXAMPLE a(11) = 4 because we have [8, 1, 1, 1], [1, 8, 1, 1], [1, 1, 8, 1] and [1, 1, 1, 8]. MAPLE b:= proc(n, t) option remember; local r, f, g;       if n=0 then t else r, f, g:=\$0..2; while f<=n       do r, f, g:= r+b(n-f, 1-t), f+3*g*(g-1)+1, g+1 od; r fi     end: a:= n-> b(n, 1): seq(a(n), n=0..60);  # Alois P. Heinz, Dec 03 2020 MATHEMATICA nmax = 57; CoefficientList[Series[(1/2) (1/(1 - Sum[x^(k^3), {k, 1, Floor[nmax^(1/3)] + 1}]) + 1/Sum[x^(k^3), {k, 0, Floor[nmax^(1/3)] + 1}]), {x, 0, nmax}], x] CROSSREFS Cf. A000578, A023358, A034008, A323633, A339368, A339418, A339421. Sequence in context: A327529 A318775 A317500 * A317494 A317505 A137374 Adjacent sequences:  A339417 A339418 A339419 * A339421 A339422 A339423 KEYWORD nonn AUTHOR Ilya Gutkovskiy, Dec 03 2020 STATUS approved

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Last modified September 27 04:10 EDT 2021. Contains 347673 sequences. (Running on oeis4.)