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A092362 Number of partitions of n^2 into squares greater than 1.

%I A092362 #16 Apr 10 2017 12:25:14
%S A092362 1,0,1,1,2,3,5,8,11,28,44,94,167,354,643,1314,2412,4792,8981,17374,
%T A092362 32566,62008,115702,217040,402396,745795,1372266,2517983,4595652,
%U A092362 8354350,15125316,27265107,48972467,87584837,156119631,277152178,490437445,864534950
%N A092362 Number of partitions of n^2 into squares greater than 1.
%C A092362 a(n) = A078134(A000290(n)).
%H A092362 Alois P. Heinz, <a href="/A092362/b092362.txt">Table of n, a(n) for n = 0..500</a>
%F A092362 a(n) ~ exp(3*Pi^(1/3) * Zeta(3/2)^(2/3) * n^(2/3) / 2^(4/3)) * Zeta(3/2)^(4/3) / (2^(11/3) * sqrt(3) * Pi^(5/6) * n^(11/3)). - _Vaclav Kotesovec_, Apr 10 2017
%e A092362 a(6) = 5: 6^2 = 36 = 16+16+4 = 16+4+4+4+4+4 = 9+9+9+9 = 4+4+4+4+4+4+4+4+4.
%p A092362 b:=proc(n, i) option remember; `if`(n=0, 1,
%p A092362      `if`(i<2, 0, b(n, i-1) +`if`(i^2>n, 0, b(n-i^2, i))))
%p A092362    end:
%p A092362 a:= n-> b(n^2, n):
%p A092362 seq(a(n), n=0..50);  # _Alois P. Heinz_, Apr 15 2013
%t A092362 b[n_, i_] := b[n, i] = If[n == 0, 1, If[i<2, 0, b[n, i-1] + If[i^2>n, 0, b[n-i^2, i]]]]; a[n_] := b[n^2, n]; Table[a[n], {n, 0, 50}] (* _Jean-François Alcover_, Nov 11 2015, after _Alois P. Heinz_ *)
%Y A092362 Cf. A001156, A037444.
%Y A092362 Cf. A093115, A093116.
%K A092362 nonn
%O A092362 0,5
%A A092362 _Reinhard Zumkeller_, Mar 19 2004
%E A092362 Corrected a(0) and more terms from _Alois P. Heinz_, Apr 15 2013