A171099 a(n) = number of solutions (x,y) (with 0 <= x <= y) to x*(x+1)/2 + y*(y+1)/2 = n!.

1, 1, 1, 2, 1, 2, 0, 1, 1, 1, 2, 0, 0, 1, 0, 2, 1, 2, 0, 0, 0, 2, 0, 0, 2, 0, 0, 8, 1, 2, 0, 0, 4, 4, 16, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 1, 0, 0, 0, 0, 32, 0, 0, 0, 0, 0, 0, 2, 0, 16, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 16, 2, 4, 0, 0, 0, 2, 1, 0, 0, 0, 0, 0, 0

Offset

0,4

Links

Table of n, a(n) for n=0..92.

Formula

a(n) = A000161(8*n! + 2). - Max Alekseyev, Dec 12 2011

Example

Initial solutions: (x,y,n) = (0,1,0), (0,1,1), (1,1,2), (0,3,3), (2,2,3), (2,6,4), (0,15,5), (5,14,5), (45,89,7), (89,269,8), (210,825,9), (760,2610,10), (1770,2030,10), none for n = 11 or 12, one for n = 13 (71504,85680,13) (found by Ed Pegg Jr), etc.

Crossrefs

Cf. A000161, A152089 (n for which no solutions exist), A180590 (n for which solutions exist).

Sequence in context: A120728 A092149 A303975 * A337253 A127173 A362867

Adjacent sequences: A171096 A171097 A171098 * A171100 A171101 A171102

Keyword

nonn

Author

N. J. A. Sloane, Sep 24 2010, based on a posting by R. K. Guy to the Sequence Fans Mailing List, Sep 10 2010

Extensions

Corrected and extended (with data from Georgi Guninski, at the suggestion of N. J. A. Sloane) by D. S. McNeil, Sep 26 2010

Status

approved