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Number of permutations p of (1,2,3,...,n) such that k+p(k) is a triangular number for 1<=k<=n.
0

%I #16 Mar 03 2024 03:56:38

%S 1,0,1,1,0,1,1,1,2,4,3,9,14,13,52,124,161,181,715,2338,7073,8624,

%T 15466,52858,150365,316543,691771,1681604,5324919,15407311,37417775,

%U 69725286,155786456,579599171,2600274145,10530031625,22971756045,47057778714,112946192928

%N Number of permutations p of (1,2,3,...,n) such that k+p(k) is a triangular number for 1<=k<=n.

%F a(n) = permanent(m), where the n X n matrix m is defined by m(i,j) = 1 or 0, depending on whether i+j is a triangular number or not.

%Y Cf. A006063, A073364, A095986, A097082, A097083, A096680.

%Y See also A000217.

%K nonn

%O 0,9

%A _Ray Chandler_, Jul 26 2004

%E More terms from _David Wasserman_, Nov 27 2007

%E a(0) and a(31)-a(38) from _Martin Ehrenstein_, Mar 03 2024