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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
OFFSET
0,11
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
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Dec 05 2020
STATUS
approved