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A093116 Number of partitions of n^2 into squares not less than n.

%I A093116 #11 Oct 26 2015 07:51:00
%S A093116 1,1,1,1,2,2,2,1,2,5,4,4,5,9,15,23,24,13,20,32,55,84,113,185,303,545,
%T A093116 167,298,435,716,1055,1701,2584,4213,6471,10218,15884,4856,7376,11231,
%U A093116 17221,26054,39583,60109,91622,138569,209951,318368,483098,730183
%N A093116 Number of partitions of n^2 into squares not less than n.
%H A093116 Alois P. Heinz, <a href="/A093116/b093116.txt">Table of n, a(n) for n = 0..250</a>
%e A093116 n=10: 10^2 = 100 = 64+36 = 36+16+16+16+16 = 25+25+25+25, all other partitions of 100 into squares contain parts < 10, therefore a(10) = 4.
%p A093116 b:= proc(n, i) option remember; `if`(n=0, 1,
%p A093116      `if`(i^2>n, 0, b(n, i+1) +b(n-i^2, i)))
%p A093116     end:
%p A093116 a:= proc(n) local r; r:= isqrt(n);
%p A093116       b(n^2, r+`if`(r^2<n, 1, 0))
%p A093116     end:
%p A093116 seq(a(n), n=0..50);  # _Alois P. Heinz_, Apr 15 2013
%t A093116 b[n_, i_] := b[n, i] = If[n==0, 1, If[i^2>n, 0, b[n, i+1] + b[n-i^2, i]]]; a[n_] := With[{r = Sqrt[n]//Floor}, b[n^2, r + If[r^2<n, 1, 0]]]; Table[ a[n], {n, 0, 50}] (* _Jean-François Alcover_, Oct 26 2015, after _Alois P. Heinz_ *)
%Y A093116 Cf. A093115, A092362, A001156, A037444, A078134.
%Y A093116 Cf. A072213, A161408. [_Reinhard Zumkeller_, Jun 10 2009]
%K A093116 nonn
%O A093116 0,5
%A A093116 _Reinhard Zumkeller_, Mar 21 2004