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A030273
Number of partitions of n^2 into distinct squares.
15
1, 1, 1, 1, 1, 2, 1, 2, 1, 3, 3, 4, 2, 7, 8, 12, 13, 16, 25, 28, 55, 51, 91, 90, 158, 176, 288, 297, 487, 521, 847, 908, 1355, 1580, 2175, 2744, 3636, 4452, 5678, 7385, 9398, 11966, 14508, 19322, 23065, 31301, 36177, 49080, 57348, 77446, 91021, 121113, 141805
OFFSET
0,6
LINKS
Alois P. Heinz and Vaclav Kotesovec, Table of n, a(n) for n = 0..1000 (terms 0..750 from Alois P. Heinz)
FORMULA
a(n) = [x^(n^2)] Product_{k>=1} (1 + x^(k^2)). - Ilya Gutkovskiy, Apr 13 2017
MAPLE
b:= proc(n, i) option remember; `if`(n=0, 1,
`if`(n>i*(i+1)*(2*i+1)/6, 0, b(n, i-1)+
`if`(i^2>n, 0, b(n-i^2, i-1))))
end:
a:= n-> b(n^2, n):
seq(a(n), n=0..50); # Alois P. Heinz, Nov 20 2012
MATHEMATICA
b[n_, i_] := b[n, i] = If[n==0, 1, If[n > i*(i+1)*(2*i+1)/6, 0, b[n, i-1] +If[i^2 > n, 0, b[n-i^2, i-1]]]]; a[n_] := b[n^2, n]; Table[a[n], {n, 0, 50}] (* Jean-François Alcover, Jul 30 2015, after Alois P. Heinz *)
PROG
(Haskell)
a030273 n = p (map (^ 2) [1..]) (n^2) where
p _ 0 = 1
p (k:ks) m | m < k = 0
| otherwise = p ks (m - k) + p ks m
-- Reinhard Zumkeller, Aug 14 2011
CROSSREFS
KEYWORD
nonn
EXTENSIONS
a(0)=1 prepended by Alois P. Heinz, Feb 18 2015
STATUS
approved