

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, 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
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OFFSET

0,4


LINKS

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


FORMULA

a(n) = A000161(8*n!+2).  Max Alekseyev


EXAMPLE

Initial solutions are: (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 * A127173 A035160 A027414
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 G. Guninski, at the suggestion of N. J. A. Sloane) by D. S. McNeil, Sep 26 2010


STATUS

approved



