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Number of ways to reciprocally link elements of an 4Xn array either to themselves or to exactly two horizontal, diagonal or antidiagonal neighbors
1

%I #4 Dec 18 2012 09:46:34

%S 1,8,126,2586,52189,1071230,21914482,449023031,9196824619,

%T 188399767218,3859260231149,79056143231850,1619440886287615,

%U 33173815285042631,679556410727542259,13920527633029367143,285158193122827850868

%N Number of ways to reciprocally link elements of an 4Xn array either to themselves or to exactly two horizontal, diagonal or antidiagonal neighbors

%C Row 4 of A220725

%H R. H. Hardin, <a href="/A220728/b220728.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 20*a(n-1) +55*a(n-2) -913*a(n-3) -294*a(n-4) +1396*a(n-5) +6052*a(n-6) +11468*a(n-7) -1929*a(n-8) -29156*a(n-9) -69229*a(n-10) +5550*a(n-11) +77439*a(n-12) +61760*a(n-13) -10148*a(n-14) -26093*a(n-15) -24390*a(n-16) -1213*a(n-17) +12028*a(n-18) -1380*a(n-19) +1823*a(n-20) -1197*a(n-21) +66*a(n-22) +47*a(n-23) -13*a(n-24) +2*a(n-25)

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

%e .00.79.00...00.69.47...69.47.00...69.49.00...00.67.47...69.49.00...00.79.00

%e .36.46.14...00.36.14...36.14.00...00.16.14...36.34.00...00.17.17...36.46.14

%e .00.69.47...69.49.00...69.49.00...00.79.00...69.47.00...39.39.00...69.46.47

%e .00.36.14...00.16.14...00.16.14...36.46.14...36.14.00...00.16.14...00.13.00

%K nonn

%O 1,2

%A _R. H. Hardin_ Dec 18 2012