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%I #7 Jun 18 2017 12:45:04
%S 1,4,27,406,12180,550173,18314708,1182352612,291282493174,
%T 42207024086536,2070868688611599,493143363040812884,
%U 933291694075331622647,530152639533410371743176,60230981411511158858617306,63827420909748305015725846472,911985479463119474886614252798296
%N 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 7 elements linked to themselves.
%C Column 7 of A271617.
%F a(n) = Sum_{i=0..3} A288852(n,floor(n*(n+1)/4)-i). - _Alois P. Heinz_, Jun 18 2017
%e Some solutions for n=4
%e .....6........6........0........0........0........6........0........5
%e ....0.1......6.1......4.3......4.3......0.6......0.1......0.5......2.5
%e ...5.6.0....6.1.0....0.6.6....0.6.0....0.0.1....4.3.0....5.2.6....0.2.5
%e ..2.0.1.0..0.1.4.3..4.3.1.1..0.0.1.0..4.3.4.3..0.4.3.0..2.0.0.1..0.0.2.0
%e Element moves: 0=itself 1=nw 2=ne 3=w 4=e 5=sw 6=se, reciprocals total 7
%Y Cf. A271617, A288852.
%K nonn
%O 1,2
%A _R. H. Hardin_, Apr 10 2016
%E a(14)-a(17) from _Alois P. Heinz_, Jun 15 2017
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