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A220685 Number of ways to reciprocally link elements of an nX5 array either to themselves or to exactly two horizontal, vertical or antidiagonal neighbors 1

%I #4 Dec 17 2012 19:23:15

%S 1,114,5851,312603,15978924,822649205,42362190063,2181341369109,

%T 112319870453715,5783510938076077,297801401665428743,

%U 15334225523450669062,789581475759386788696,40656693721278204870112

%N Number of ways to reciprocally link elements of an nX5 array either to themselves or to exactly two horizontal, vertical or antidiagonal neighbors

%C Column 5 of A220688

%H R. H. Hardin, <a href="/A220685/b220685.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 35*a(n-1) +673*a(n-2) +8237*a(n-3) +46927*a(n-4) -112480*a(n-5) -3992526*a(n-6) -35333024*a(n-7) -169366609*a(n-8) -361164394*a(n-9) +47195630*a(n-10) +13502054*a(n-11) +495005695*a(n-12) +6209070799*a(n-13) +5791334536*a(n-14) -11945755468*a(n-15) -10812604841*a(n-16) +3004142790*a(n-17) -8986269878*a(n-18) +26749603735*a(n-19) -17268218707*a(n-20) +10625240169*a(n-21) +1286966410*a(n-22) -5196232889*a(n-23) -236330168*a(n-24) +3747662678*a(n-25) -4565014033*a(n-26) +2769440835*a(n-27) -1086425818*a(n-28) +220144889*a(n-29) -12788683*a(n-30) -5653764*a(n-31) +2046130*a(n-32) -331034*a(n-33) +12027*a(n-34) +3632*a(n-35) +36*a(n-36) for n>37

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

%e .00.78.68.48.78...00.67.46.46.48...00.00.00.68.48...00.78.68.47.00

%e .36.24.28.23.27...38.68.48.68.24...00.78.00.28.28...38.27.23.78.00

%e .00.00.26.34.00...26.24.26.24.00...36.24.00.26.24...23.00.36.24.00

%K nonn

%O 1,2

%A _R. H. Hardin_ Dec 17 2012

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