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 A339442 Number of compositions (ordered partitions) of n into an odd number of distinct triangular numbers. 2
 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 7, 0, 0, 0, 6, 1, 0, 6, 0, 12, 0, 1, 6, 0, 6, 6, 6, 0, 13, 0, 6, 6, 12, 0, 6, 126, 1, 18, 0, 12, 6, 126, 6, 6, 12, 7, 132, 6, 120, 18, 126, 0, 24, 246, 12, 127, 126, 126, 12, 132, 126, 138, 126, 132, 12, 246, 133, 138, 366, 6, 258, 252 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,11 LINKS Alois P. Heinz, Table of n, a(n) for n = 0..10000 EXAMPLE a(19) = 12 because we have [15, 3, 1] (6 permutations) and [10, 6, 3] (6 permutations). MAPLE b:= proc(n, i, p) option remember; `if`(n=0, irem(p, 2)*p!, (t->      `if`(t>n, 0, b(n, i+1, p)+b(n-t, i+1, p+1)))(i*(i+1)/2))     end: a:= n-> b(n, 1, 0): seq(a(n), n=0..100);  # Alois P. Heinz, Dec 05 2020 MATHEMATICA b[n_, i_, p_] := b[n, i, p] = If[n == 0, Mod[p, 2]*p!, With[{t = i(i+1)/2}, If[t > n, 0, b[n, i + 1, p] + b[n - t, i + 1, p + 1]]]]; a[n_] := b[n, 1, 0]; a /@ Range[0, 100] (* Jean-François Alcover, Mar 14 2021, after Alois P. Heinz *) CROSSREFS Cf. A000217, A331843, A332304, A339376, A339417, A339441. Sequence in context: A306755 A005070 A135435 * A331748 A171917 A198919 Adjacent sequences:  A339439 A339440 A339441 * A339443 A339444 A339445 KEYWORD nonn AUTHOR Ilya Gutkovskiy, Dec 05 2020 STATUS approved

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Last modified September 20 10:18 EDT 2021. Contains 347584 sequences. (Running on oeis4.)