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%I #5 Mar 21 2015 06:11:51
%S 1,1,2,2,2,5,4,7,11,12,15,29,31,45,67,77,105,161,187,260,352,431,577,
%T 801,950,1279,1676,2074,2706,3514,4287,5596,7128,8782
%N Number of partitions of 2n for which the square of the largest part equals the sum of the squares of the other parts.
%C There are no such partitions of 2n+1.
%e For n=6 the five partitions {6,6}, {5,4,3}, {4,3,2,1,1,1}, {4,2,2,2,2} and {3,1,1,1,1,1,1,1,1,1} and no others, satisfy the stated requirements, so a(12)=5.
%t (* first do *) Needs["DiscreteMath`Combinatorica`"] (* then *) f[n_] := Block[{p = Partitions[n], l = PartitionsP[n], c = 0, k = 2}, While[k < l + 1, If[ p[[k, 1]]^2 == Plus @@ (Drop[p[[k]], 1]^2), c++ ]; k++ ]; c]; Table[ f[n], {n, 67}] (* _Robert G. Wilson v_, Sep 23 2004 *)
%K nonn
%O 1,3
%A _John W. Layman_, Sep 22 2004
%E More terms from _Robert G. Wilson v_, Sep 23 2004
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