

A098101


Number of partitions of 2n for which the square of the largest part equals the sum of the squares of the other parts.


0



1, 1, 2, 2, 2, 5, 4, 7, 11, 12, 15, 29, 31, 45, 67, 77, 105, 161, 187, 260, 352, 431, 577, 801, 950, 1279, 1676, 2074, 2706, 3514, 4287, 5596, 7128, 8782
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OFFSET

1,3


COMMENTS

There are no such partitions of 2n+1.


LINKS

Table of n, a(n) for n=1..34.


EXAMPLE

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.


MATHEMATICA

(* 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 *)


CROSSREFS

Sequence in context: A285704 A058704 A316660 * A257670 A105960 A081290
Adjacent sequences: A098098 A098099 A098100 * A098102 A098103 A098104


KEYWORD

nonn


AUTHOR

John W. Layman, Sep 22 2004


EXTENSIONS

More terms from Robert G. Wilson v, Sep 23 2004


STATUS

approved



