%I #6 Jan 20 2024 15:17:13
%S 1,1,1,1,8,1,1,33,33,1,1,155,423,155,1,1,710,6156,6156,710,1,1,3265,
%T 87542,308246,87542,3265,1,1,15009,1250507,14637699,14637699,1250507,
%U 15009,1,1,68992,17847210,702811381,2255735554,702811381,17847210,68992
%N T(n,k) = Number of ways to reciprocally link elements of an n X k array either to themselves or to exactly two king-move neighbors.
%C Table starts
%C .1.......1...........1..............1................1.................1
%C .1.......8..........33............155..............710..............3265
%C .1......33.........423...........6156............87542...........1250507
%C .1.....155........6156.........308246.........14637699.........702811381
%C .1.....710.......87542.......14637699.......2255735554......353961472626
%C .1....3265.....1250507......702811381.....353961472626...182840438017294
%C .1...15009....17847210....33667621356...55328483420671.93925801702787503
%C .1...68992...254759570..1613595307718.8656054653129245
%C .1..317149..3636434730.77327320807492
%C .1.1457879.51906768670
%C .1.6701646
%C .1
%H R. H. Hardin, <a href="/A220595/b220595.txt">Table of n, a(n) for n = 1..84</a>
%e Some solutions for n=3 k=4 0=self 1=nw 2=n 3=ne 4=w 6=e 7=sw 8=s 9=se (reciprocal directions total 10).
%e .89.79.69.48...00.68.48.00...00.79.67.47...68.47.78.00...00.00.69.48
%e .23.16.14.12...00.28.26.47...39.37.13.00...23.38.28.00...89.79.78.12
%e .00.00.00.00...00.26.34.00...36.14.00.00...00.26.24.00...23.13.12.00
%K nonn,tabl
%O 1,5
%A _R. H. Hardin_, Dec 16 2012