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%I #11 Jun 18 2017 13:13:15
%S 1,1,3,1,3,2,1,4,17,6,1,4,17,114,240,1,4,26,114,240,2238,1,4,26,307,
%T 2571,2238,2196,1,4,27,307,2571,42702,216318,37004,1,4,27,406,7764,
%U 42702,216318,5622392,20454036,1,4,27,406,7764,222936,3243689,5622392,20454036,970623228
%N T(n,k) = Number of ways to reciprocally link elements of an n X n X n triangular array with themselves or a neighbor, with no more than k elements linked to themselves.
%C Table starts
%C ........1........1..........1..........1...........1...........1............1
%C ........3........3..........4..........4...........4...........4............4
%C ........2.......17.........17.........26..........26..........27...........27
%C ........6......114........114........307.........307.........406..........406
%C ......240......240.......2571.......2571........7764........7764........12180
%C .....2238.....2238......42702......42702......222936......222936.......550173
%C .....2196...216318.....216318....3243689.....3243689....18314708.....18314708
%C ....37004..5622392....5622392..132728354...132728354..1182352612...1182352612
%C .20454036.20454036.1491326272.1491326272.30892003921.30892003921.291282493174
%H Alois P. Heinz, <a href="/A271617/b271617.txt">Antidiagonals n = 1..20, flattened</a> (first 16 antidiagonals from R. H. Hardin)
%e Some solutions for n=4 k=4
%e .....5........5........0........5........0........6........5........5
%e ....2.0......2.0......0.5......2.0......6.0......5.1......2.0......2.6
%e ...6.6.6....0.5.5....5.2.5....0.0.0....0.1.6....2.0.0....5.4.3....5.5.1
%e ..0.1.1.1..0.2.2.0..2.0.2.0..4.3.4.3..0.4.3.1..0.4.3.0..2.0.4.3..2.2.4.3
%e Element moves: 0=itself 1=nw 2=ne 3=w 4=e 5=sw 6=se, reciprocals total 7
%K nonn,tabl
%O 1,3
%A _R. H. Hardin_, Apr 10 2016
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