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%I #19 Jun 27 2022 23:49:09
%S 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,
%T 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,
%U 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
%N a(n) = number of solutions (x,y) (with 0 <= x <= y) to x*(x+1)/2 + y*(y+1)/2 = n!.
%F a(n) = A000161(8*n! + 2). - _Max Alekseyev_, Dec 12 2011
%e 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.
%Y Cf. A000161, A152089 (n for which no solutions exist), A180590 (n for which solutions exist).
%K nonn
%O 0,4
%A _N. J. A. Sloane_, Sep 24 2010, based on a posting by _R. K. Guy_ to the Sequence Fans Mailing List, Sep 10 2010
%E Corrected and extended (with data from _Georgi Guninski_, at the suggestion of _N. J. A. Sloane_) by _D. S. McNeil_, Sep 26 2010
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