A339441 Number of compositions (ordered partitions) of n into an even number of distinct triangular numbers.
1, 0, 0, 0, 2, 0, 0, 2, 0, 2, 0, 2, 0, 2, 0, 0, 4, 0, 2, 0, 24, 2, 2, 0, 2, 26, 0, 2, 0, 26, 0, 28, 24, 0, 26, 24, 2, 2, 50, 2, 48, 0, 26, 26, 0, 48, 28, 72, 2, 26, 48, 4, 48, 48, 24, 74, 770, 2, 50, 48, 50, 26, 72, 720, 98, 74, 26, 74, 48, 770, 74, 768, 26, 122, 792, 72
Offset: 0
Keywords
Examples
a(20) = 24 because we have [10, 6, 3, 1] (24 permutations).
Links
Programs
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Maple
b:= proc(n, i, p) option remember; `if`(n=0, irem(1+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[1 + 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 *)