A331983 Number of compositions (ordered partitions) of n into distinct squares > 1.
1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 0, 3, 0, 0, 0, 8, 0, 0, 0, 0, 2, 0, 1, 0, 6, 0, 2, 2, 0, 0, 0, 8, 0, 0, 0, 7, 6, 0, 2, 2, 24, 0, 6, 0, 2, 0, 0, 8, 6, 0, 1, 32, 0, 0, 2, 6, 6, 0, 0, 2, 32, 0, 0, 12, 30, 0, 2
Offset: 0
Keywords
Examples
a(25) = 3 because we have [25], [16, 9] and [9, 16].
Links
Crossrefs
Programs
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Maple
b:= proc(n, i, p) option remember; `if`(n=0, p!, `if`(i*(i+1)*(2*i+1)/6-1
n, 0, b(n-i^2, i-1, p+1))+b(n, i-1, p))) end: a:= n-> b(n, isqrt(n), 0): seq(a(n), n=0..87); # Alois P. Heinz, Feb 03 2020 -
Mathematica
b[n_, i_, p_] := b[n, i, p] = If[n == 0, p!, If[i(i+1)(2i+1)/6 - 1 < n, 0, If[i^2 > n, 0, b[n - i^2, i - 1, p + 1]] + b[n, i - 1, p]]]; a[n_] := b[n, Floor@Sqrt[n], 0]; a /@ Range[0, 87] (* Jean-François Alcover, Nov 26 2020, after Alois P. Heinz *)