A220714 - OEIS

A220714

Number of ways to reciprocally link elements of an n X 3 array either to themselves or to exactly two king-move neighbors, without consecutive collinear links.

%I #6 Apr 13 2022 20:12:59

%S 1,26,226,2243,21195,201598,1913495,18172469,172565016,1638746380,

%T 15562024443,147782179281,1403387239808,13327022602525,

%U 126557734357659,1201833388741096,11413000424299772,108381561410710361

%N Number of ways to reciprocally link elements of an n X 3 array either to themselves or to exactly two king-move neighbors, without consecutive collinear links.

%C Column 3 of A220718.

%H R. H. Hardin, <a href="/A220714/b220714.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 7*a(n-1) +31*a(n-2) -61*a(n-3) -118*a(n-4) +346*a(n-5) +321*a(n-6) -404*a(n-7) -191*a(n-8) -429*a(n-9) -270*a(n-10) +1567*a(n-11) -1015*a(n-12) -504*a(n-13) +179*a(n-14) -554*a(n-15) +136*a(n-16) +185*a(n-17) -21*a(n-18) -3*a(n-19) -a(n-20).

%e Some solutions for n=3 0=self 1=nw 2=n 3=ne 4=w 6=e 7=sw 8=s 9=se (reciprocal directions total 10)

%e .00.67.48...68.47.00...68.48.00...89.69.48...00.78.00...68.48.00...69.47.00

%e .38.68.24...23.79.78...29.26.47...26.14.12...39.29.78...26.24.78...38.17.00

%e .26.24.00...36.34.12...00.13.00...00.00.00...00.13.12...00.36.24...23.00.00

%Y Cf. A220718.

%K nonn

%O 1,2

%A _R. H. Hardin_, Dec 18 2012