A095809 Least positive number having exactly n partitions into three squares.

1, 9, 41, 81, 146, 194, 306, 369, 425, 594, 689, 866, 1109, 1161, 1154, 1361, 1634, 1781, 1889, 2141, 2729, 2609, 3626, 3366, 3566, 3449, 3506, 4241, 4289, 4826, 5066, 5381, 7034, 5561, 6254, 7229, 7829, 8186, 8069, 8126, 8609, 8921, 8774, 10386

Offset

1,2

Comments

Note that a square can be zero.

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..200

Example

41 is the least number having three partitions: 41 = 0+16+25 = 1+4+36 = 9+16+16.

Mathematica

lim=200; nLst=Table[0, {lim^2}]; Do[n=a^2+b^2+c^2; If[n>0 && n<lim^2, nLst[[n]]++ ], {a, 0, lim}, {b, a, Sqrt[lim^2-a^2]}, {c, b, Sqrt[lim^2-a^2-b^2]}]; u=Union[nLst]; kMax=First[Complement[1+Range[u[[ -1]]], u]]-1; Table[First[Flatten[Position[nLst, k]]], {k, kMax}]

Crossrefs

Apart from initial term, same as A000437.

Cf. A094739 (n having a unique partition into three squares), A095811 (greatest number having exactly n partitions into three squares).

Sequence in context: A198943 A000451 A000437 * A273359 A251422 A018836

Adjacent sequences: A095806 A095807 A095808 * A095810 A095811 A095812

Keyword

nonn

Author

T. D. Noe, Jun 07 2004

Status

approved