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A220637 Number of ways to reciprocally link elements of an 7Xn array either to themselves or to exactly two horizontal or antidiagonal neighbors.

%I A220637 #6 Jul 23 2025 01:19:51
%S A220637 1,1,21,1081,49448,1932695,72097810,2685329069,100377946990,
%T A220637 3759405889469,140807441642550,5273589943694582,197503772671988555,
%U A220637 7396752550237211667,277016765034509275485,10374589395033217351070
%N A220637 Number of ways to reciprocally link elements of an 7Xn array either to themselves or to exactly two horizontal or antidiagonal neighbors.
%C A220637 Row 7 of A220632
%H A220637 R. H. Hardin, <a href="/A220637/b220637.txt">Table of n, a(n) for n = 1..210</a>
%F A220637 Empirical: a(n) = 64*a(n-1) -919*a(n-2) -8570*a(n-3) +216353*a(n-4) +531044*a(n-5) -21261655*a(n-6) -32609802*a(n-7) +1171199810*a(n-8) +2109648488*a(n-9) -39063293438*a(n-10) -92688824988*a(n-11) +805714999129*a(n-12) +2451647584900*a(n-13) -10235971284893*a(n-14) -39686089670614*a(n-15) +77545474788177*a(n-16) +406392430654220*a(n-17) -310370552865987*a(n-18) -2718695732195110*a(n-19) +210699841602232*a(n-20) +12228246476518236*a(n-21) +4161966890556370*a(n-22) -37977869919855064*a(n-23) -22915950784622786*a(n-24) +83551109201976972*a(n-25) +64155355218097920*a(n-26) -133459785405218204*a(n-27) -114791737399493541*a(n-28) +158383696504733072*a(n-29) +141093830957446007*a(n-30) -142389992780977126*a(n-31) -123172425999322826*a(n-32) +98262359403451972*a(n-33) +77694058934774432*a(n-34) -52288937671239360*a(n-35) -35710455324063520*a(n-36) +21366553927398268*a(n-37) +11998414558707900*a(n-38) -6636734211915116*a(n-39) -2945615880166783*a(n-40) +1547201872012720*a(n-41) +525999708944081*a(n-42) -266869650005278*a(n-43) -67611096067185*a(n-44) +33461039766336*a(n-45) +6135683963135*a(n-46) -2975024785990*a(n-47) -380281115163*a(n-48) +180562165772*a(n-49) +15221629883*a(n-50) -7030915042*a(n-51) -357383528*a(n-52) +157690672*a(n-53) +4153756*a(n-54) -1668248*a(n-55) -18816*a(n-56) +6272*a(n-57) for n>63
%e A220637 Some solutions for n=3 0=self 3=ne 4=w 6=e 7=sw (reciprocal directions total 10)
%e A220637 .00.00.00...00.00.00...00.67.47...00.00.00...00.67.47...00.00.00...00.00.00
%e A220637 .00.00.00...00.67.47...36.34.00...00.00.00...36.34.00...00.67.47...00.00.00
%e A220637 .00.00.00...36.34.00...00.00.00...00.67.47...00.67.47...36.34.00...00.00.00
%e A220637 .00.00.00...00.00.00...00.67.47...36.34.00...36.34.00...00.00.00...00.00.00
%e A220637 .00.67.47...00.00.00...36.34.00...00.67.47...00.67.47...00.00.00...00.00.00
%e A220637 .36.34.00...00.67.47...00.67.47...36.34.00...36.34.00...00.00.00...00.67.47
%e A220637 .00.00.00...36.34.00...36.34.00...00.00.00...00.00.00...00.00.00...36.34.00
%K A220637 nonn
%O A220637 1,3
%A A220637 _R. H. Hardin_ Dec 17 2012