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A220715 Number of ways to reciprocally link elements of an nX4 array either to themselves or to exactly two king-move neighbors, without consecutive collinear links 1

%I

%S 1,118,2243,72923,2126423,63806966,1902974315,56814065240,

%T 1695753689937,50616199772781,1510818091855523,45095791460540255,

%U 1346044870553900218,40177524253586319614,1199241822560808863212,35795659984527447229283

%N Number of ways to reciprocally link elements of an nX4 array either to themselves or to exactly two king-move neighbors, without consecutive collinear links

%C Column 4 of A220718

%H R. H. Hardin, <a href="/A220715/b220715.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 27*a(n-1) +218*a(n-2) -4167*a(n-3) -2238*a(n-4) +279765*a(n-5) -837556*a(n-6) -9510069*a(n-7) +51706001*a(n-8) +170902685*a(n-9) -1379270603*a(n-10) -2916930858*a(n-11) +23871214217*a(n-12) +48592745276*a(n-13) -298839593926*a(n-14) -429563948989*a(n-15) +2118042013180*a(n-16) +3879992721463*a(n-17) -18932568794516*a(n-18) +5172886486038*a(n-19) +48756445038822*a(n-20) +9597136541026*a(n-21) -41796254756289*a(n-22) -896030877308524*a(n-23) +1207224499666967*a(n-24) +3111135194463020*a(n-25) -1604076203019642*a(n-26) -15273373653497609*a(n-27) -10825292853008442*a(n-28) +81352919819320477*a(n-29) +34933338667422793*a(n-30) -143384540350983525*a(n-31) -385018692637254330*a(n-32) +308969134164070030*a(n-33) +1717971050198499504*a(n-34) -1564322409532992905*a(n-35) -2986300709023877703*a(n-36) +2110252700439366942*a(n-37) +5453780366327497679*a(n-38) +371316710789284744*a(n-39) -14266820049835803870*a(n-40) +821793489703620010*a(n-41) +20101913038833494061*a(n-42) -126600521568603311*a(n-43) -21586493455386361844*a(n-44) -2133427856527889127*a(n-45) +19425074896572483723*a(n-46) +2217428671242118766*a(n-47) -13966094878768033977*a(n-48) +1438576255704793871*a(n-49) +4174978235974982028*a(n-50) +1538080869042294965*a(n-51) -17129837797868140650*a(n-52) +32360333812276354278*a(n-53) -9761802512302820845*a(n-54) -37046343187525306954*a(n-55) +38590238998125051624*a(n-56) -10645213180052535365*a(n-57) +19247049676319604348*a(n-58) -30460679562886114932*a(n-59) +11473284550788820469*a(n-60) +2653613573023586974*a(n-61) -2845704340430549512*a(n-62) +2351965695570937626*a(n-63) -3994448694896953184*a(n-64) +3426390086734421544*a(n-65) -1570449846470389084*a(n-66) +1687013684172456220*a(n-67) -767997366767314992*a(n-68) -171849877273372592*a(n-69) +13888647368350704*a(n-70) -68870557102727648*a(n-71) +126980968396773696*a(n-72) -98731887707797568*a(n-73) +50215450311674752*a(n-74) -9026127145861376*a(n-75) +1020535271492608*a(n-76) -280997983232000*a(n-77) -57798187278336*a(n-78) -16904717058048*a(n-79) +14172273278976*a(n-80) -957233561600*a(n-81) -80442294272*a(n-82) -811597824*a(n-83)

%e Some solutions for n=3 0=self 1=nw 2=n 3=ne 4=w 6=e 7=sw 8=s 9=se (reciprocal directions total 10)

%e .69.48.89.00...89.00.89.00...00.00.69.47...69.47.00.00...00.00.69.47

%e .00.12.26.14...29.18.29.18...89.00.38.18...38.18.68.47...89.78.36.14

%e .00.00.00.00...00.12.00.12...26.14.26.24...26.24.23.00...23.12.00.00

%K nonn

%O 1,2

%A _R. H. Hardin_ Dec 18 2012

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Last modified January 17 11:27 EST 2022. Contains 350394 sequences. (Running on oeis4.)