A098101 Number of partitions of 2n for which the square of the largest part equals the sum of the squares of the other parts.

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

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 A346426 A105960

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