%I
%S 1,4,26,307,7764,222936,3243689,132728354,30892003921,3065366376540,
%T 74672717363118,12952235029243936,25923218026065797712,
%U 11188107558636007931696,695394278635888843298780,579704015638436450676621584,9319830273030294425399538816052
%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 5 elements linked to themselves.
%C Column 5 of A271617.
%F a(n) = Sum_{i=0..2} A288852(n,floor(n*(n+1)/4)i).  _Alois P. Heinz_, Jun 18 2017
%e Some solutions for n=4
%e .....5........0........6........0........0........0........5........5
%e ....2.0......0.0......0.1......4.3......4.3......0.5......2.5......2.0
%e ...4.3.5....4.3.5....0.4.3....4.3.6....0.4.3....0.2.5....5.2.5....0.0.6
%e ..0.0.2.0..4.3.2.0..0.4.3.0..0.0.0.1..0.0.4.3..4.3.2.0..2.0.2.0..0.4.3.1
%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
