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A030273 Number of partitions of n^2 into distinct squares. 6
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-Fran├žois 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

Cf. A037444, A033461, A000009, A000290.

Sequence in context: A029334 A275078 A286478 * A029197 A029174 A058753

Adjacent sequences:  A030270 A030271 A030272 * A030274 A030275 A030276

KEYWORD

nonn

AUTHOR

Warren D. Smith

EXTENSIONS

a(0)=1 prepended by Alois P. Heinz, Feb 18 2015

STATUS

approved

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Last modified August 21 01:18 EDT 2017. Contains 290855 sequences.