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A331844
Number of compositions (ordered partitions) of n into distinct squares.
18
1, 1, 0, 0, 1, 2, 0, 0, 0, 1, 2, 0, 0, 2, 6, 0, 1, 2, 0, 0, 2, 6, 0, 0, 0, 3, 8, 0, 0, 8, 30, 0, 0, 0, 2, 6, 1, 2, 6, 24, 2, 8, 6, 0, 0, 8, 30, 0, 0, 7, 32, 24, 2, 8, 30, 120, 6, 24, 2, 6, 0, 8, 36, 24, 1, 34, 150, 0, 2, 12, 30, 24, 0, 2, 38, 150, 0, 12, 78, 144, 2
OFFSET
0,6
EXAMPLE
a(14) = 6 because we have [9,4,1], [9,1,4], [4,9,1], [4,1,9], [1,9,4] and [1,4,9].
MAPLE
b:= proc(n, i, p) option remember;
`if`(i*(i+1)*(2*i+1)/6<n, 0, `if`(n=0, p!,
`if`(i^2>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..82); # Alois P. Heinz, Jan 30 2020
MATHEMATICA
b[n_, i_, p_] := b[n, i, p] = If[i(i+1)(2i+1)/6 < n, 0, If[n == 0, p!, If[i^2 > n, 0, b[n - i^2, i - 1, p + 1]] + b[n, i - 1, p]]];
a[n_] := b[n, Sqrt[n] // Floor, 0];
a /@ Range[0, 82] (* Jean-François Alcover, Oct 29 2020, after Alois P. Heinz *)
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Jan 29 2020
STATUS
approved