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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 (list; graph; refs; listen; history; text; internal format)
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
Sequence in context: A275078 A286478 A340756 * A029197 A029174 A058753
KEYWORD
nonn
AUTHOR
EXTENSIONS
a(0)=1 prepended by Alois P. Heinz, Feb 18 2015
STATUS
approved

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Last modified February 27 14:28 EST 2024. Contains 370376 sequences. (Running on oeis4.)