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A025424 Number of partitions of n into 9 squares.

%I A025424 #19 Aug 19 2020 15:44:57
%S A025424 1,1,1,1,2,2,2,2,3,4,3,3,4,4,4,4,5,6,6,5,7,7,7,7,8,9,9,9,9,11,11,10,
%T A025424 12,13,12,12,15,14,16,15,15,18,17,16,18,20,19,20,20,21,23,21,23,26,28,
%U A025424 25,27,29,28,28,28,30,33,33,30,36,35,33,38,37,40,40,41,40,44,42,41,47,48,47,48
%N A025424 Number of partitions of n into 9 squares.
%H A025424 Alois P. Heinz, <a href="/A025424/b025424.txt">Table of n, a(n) for n = 0..10000</a>
%p A025424 b:= proc(n, i, t) option remember; `if`(n=0, 1,
%p A025424       `if`(i<1 or t<1, 0, b(n, i-1, t)+
%p A025424       `if`(i^2>n, 0, b(n-i^2, i, t-1))))
%p A025424     end:
%p A025424 a:= n-> b(n, isqrt(n), 9):
%p A025424 seq(a(n), n=0..120);  # _Alois P. Heinz_, May 30 2014
%t A025424 b[n_, i_, t_] := b[n, i, t] = If[n == 0, 1, If[i<1 || t<1, 0, b[n, i-1, t] + If[i^2 > n, 0, b[n-i^2, i, t-1]]]]; a[n_] := b[n, Sqrt[n] // Floor, 9]; Table[a[n], {n, 0, 120}] (* _Jean-François Alcover_, Jun 11 2015, after _Alois P. Heinz_ *)
%K A025424 nonn
%O A025424 0,5
%A A025424 _David W. Wilson_