A220735 - OEIS

A220735

Number of ways to reciprocally link elements of an nX5 array either to themselves or to exactly two horizontal, diagonal and antidiagonal neighbors, without consecutive collinear links

%I #4 Dec 18 2012 12:47:25

%S 1,32,487,7369,127288,2027456,32924133,534490260,8661108365,

%T 140500900684,2278575841968,36953271570273,599311228551359,

%U 9719536107936096,157630560274669449,2556437605930905145,41460052609326887864

%N Number of ways to reciprocally link elements of an nX5 array either to themselves or to exactly two horizontal, diagonal and antidiagonal neighbors, without consecutive collinear links

%C Column 5 of A220738

%H R. H. Hardin, <a href="/A220735/b220735.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 20*a(n-1) -65*a(n-2) +76*a(n-3) -1155*a(n-4) +18496*a(n-5) -70044*a(n-6) +72160*a(n-7) -378281*a(n-8) +114092*a(n-9) -564419*a(n-10) +5536756*a(n-11) +25967998*a(n-12) +37954124*a(n-13) +153656513*a(n-14) -157832972*a(n-15) -745918733*a(n-16) -1917603040*a(n-17) -4791944316*a(n-18) -4163305184*a(n-19) +6977275361*a(n-20) +12706741652*a(n-21) +68686379451*a(n-22) +126029637644*a(n-23) +62729877905*a(n-24) +70631612552*a(n-25) -248226923306*a(n-26) -788443556936*a(n-27) -938536545342*a(n-28) -49553932544*a(n-29) -87300444152*a(n-30) -1751070963072*a(n-31) +510955338150*a(n-32) +939527443832*a(n-33) -3349453802910*a(n-34) +1498736584968*a(n-35) +21039268013924*a(n-36) +20041433993432*a(n-37) -10137555492606*a(n-38) -18609838530008*a(n-39) -7234616664154*a(n-40) +12641325810368*a(n-41) +18097001487592*a(n-42) +16535299789824*a(n-43) -21228216014110*a(n-44) -51010314661528*a(n-45) +18061117651606*a(n-46) +8391340051480*a(n-47) +1477654226577*a(n-48) +11274541552932*a(n-49) -9396242028357*a(n-50) +2653547189052*a(n-51) +207617013041*a(n-52) +480000531904*a(n-53) -705614349292*a(n-54) -266915818336*a(n-55) +295072852243*a(n-56) -49147133412*a(n-57) -23941964399*a(n-58) +1948544708*a(n-59) +3237483262*a(n-60) -370954468*a(n-61) +8530157*a(n-62) +24305060*a(n-63) -31080201*a(n-64) -6824672*a(n-65) +1946900*a(n-66) -75296*a(n-67) +108077*a(n-68) -13372*a(n-69) +1151*a(n-70) +28*a(n-71) -a(n-72)

%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 .00.69.47.79.00...00.00.00.67.47...00.69.47.69.47...69.47.79.00.00

%e .00.39.13.67.14...69.47.39.39.00...00.36.14.39.17...39.13.67.14.00

%e .00.00.13.00.00...36.14.00.16.14...00.00.00.36.14...00.13.00.00.00

%K nonn

%O 1,2

%A _R. H. Hardin_ Dec 18 2012