login
A298640
Number of compositions (ordered partitions) of n^2 into squares > 1.
4
1, 0, 1, 1, 2, 8, 12, 129, 874, 9630, 167001, 3043147, 72844510, 2423789655, 106665874384, 6156805673648, 470151743582651, 47558937432498729, 6363358599941131580, 1126147544855148769425, 263646401550138303553708, 81649922556593759124887197
OFFSET
0,5
FORMULA
a(n) = [x^(n^2)] 1/(1 - Sum_{k>=2} x^(k^2)).
a(n) = A280542(A000290(n)).
EXAMPLE
a(5) = 8 because we have [25], [16, 9], [9, 16], [9, 4, 4, 4, 4], [4, 9, 4, 4, 4], [4, 4, 9, 4, 4], [4, 4, 4, 9, 4] and [4, 4, 4, 4, 9].
MAPLE
b:= proc(n) option remember; `if`(n=0, 1,
add(b(n-j^2), j=2..isqrt(n)))
end:
a:= n-> b(n^2):
seq(a(n), n=0..25); # Alois P. Heinz, Feb 05 2018
MATHEMATICA
b[n_] := b[n] = If[n == 0, 1, Sum[b[n - j^2], {j, 2, Floor @ Sqrt[n]}]];
a[n_] := b[n^2];
Table[a[n], {n, 0, 25}] (* Jean-François Alcover, May 21 2018, after Alois P. Heinz *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Jan 24 2018
STATUS
approved