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A220599 Number of ways to reciprocally link elements of an nX5 array either to themselves or to exactly two horizontal, vertical and antidiagonal neighbors, without 3-loops.

%I A220599 #6 Jul 23 2025 01:17:04
%S A220599 1,44,3469,167614,7558495,352586943,16505365334,770615995060,
%T A220599 35978245868462,1680090131446571,78453960278374893,
%U A220599 3663456651896335065,171068067072237399646,7988166245960912052019,373013938796405801398629
%N A220599 Number of ways to reciprocally link elements of an nX5 array either to themselves or to exactly two horizontal, vertical and antidiagonal neighbors, without 3-loops.
%C A220599 Column 5 of A220602
%H A220599 R. H. Hardin, <a href="/A220599/b220599.txt">Table of n, a(n) for n = 1..210</a>
%F A220599 Empirical: a(n) = 35*a(n-1) +272*a(n-2) +11994*a(n-3) +32896*a(n-4) +309375*a(n-5) -3315691*a(n-6) -30948895*a(n-7) +48954898*a(n-8) -303997468*a(n-9) -7054837583*a(n-10) +8970311702*a(n-11) +269208688675*a(n-12) +485473331607*a(n-13) -3325199930663*a(n-14) -12213275584466*a(n-15) +11311850155580*a(n-16) +90662524191083*a(n-17) +29640254006904*a(n-18) -171828097518485*a(n-19) -32539810960422*a(n-20) -260809904785074*a(n-21) -1037755295924050*a(n-22) +553074708665462*a(n-23) -932747145758344*a(n-24) +248650789049878*a(n-25) -2856020100608967*a(n-26) +2696048261973157*a(n-27) -11016912810502883*a(n-28) -5911302056186341*a(n-29) -5797765198888052*a(n-30) +2541001897271391*a(n-31) -10148136754490004*a(n-32) -3988488395563961*a(n-33) +1004749709024694*a(n-34) -2533119314782758*a(n-35) -686156967660631*a(n-36) -1408624723023117*a(n-37) -377816092283658*a(n-38) +1379263668015862*a(n-39) -377091489287888*a(n-40) +120261293265251*a(n-41) +55405553060124*a(n-42) +82537043808782*a(n-43) +34671368481870*a(n-44) -25343134847072*a(n-45) +5386072841942*a(n-46) +8703786206652*a(n-47) -4039895276276*a(n-48) -181761484032*a(n-49) +98622190896*a(n-50) -183111581472*a(n-51) +38324067200*a(n-52) -13820570688*a(n-53) +313286432*a(n-54) +186406848*a(n-55) -3648192*a(n-56) +34560*a(n-57) -27648*a(n-58)
%e A220599 Some solutions for n=3 0=self 2=n 3=ne 4=w 6=e 7=sw 8=s (reciprocal directions total 10)
%e A220599 .00.67.46.48.00...00.78.68.46.47...68.48.68.48.00...00.68.48.67.48
%e A220599 .38.00.67.24.00...38.27.27.36.47...28.28.28.28.00...00.27.23.67.24
%e A220599 .26.34.00.00.00...23.36.46.34.00...26.24.26.24.00...36.46.34.00.00
%K A220599 nonn
%O A220599 1,2
%A A220599 _R. H. Hardin_ Dec 16 2012