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A317693 Number of nX4 0..1 arrays with every element unequal to 0, 1, 3, 4, 5, 6, 7 or 8 king-move adjacent elements, with upper left element zero. 1

%I #4 Aug 04 2018 20:08:18

%S 5,21,33,141,630,2742,16008,100830,603699,3769795,24122000,151848663,

%T 958240276,6090267864,38598033209,244395851672,1550053828375,

%U 9828877818014,62296855285711,394965267640728,2504248043602690

%N Number of nX4 0..1 arrays with every element unequal to 0, 1, 3, 4, 5, 6, 7 or 8 king-move adjacent elements, with upper left element zero.

%C Column 4 of A317697.

%H R. H. Hardin, <a href="/A317693/b317693.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 12*a(n-1) -51*a(n-2) +199*a(n-3) -1045*a(n-4) +3080*a(n-5) -5824*a(n-6) +19715*a(n-7) -54217*a(n-8) +86631*a(n-9) -208898*a(n-10) +470524*a(n-11) -617540*a(n-12) +1104549*a(n-13) -1778989*a(n-14) +1697347*a(n-15) -2524942*a(n-16) +2404934*a(n-17) -1513005*a(n-18) +185991*a(n-19) +6216357*a(n-20) -6144821*a(n-21) +16299949*a(n-22) -26478742*a(n-23) +17685408*a(n-24) -35457244*a(n-25) +28422411*a(n-26) -13843492*a(n-27) +4891493*a(n-28) -9152979*a(n-29) +11561051*a(n-30) +92789965*a(n-31) +9888284*a(n-32) -76956177*a(n-33) -142623604*a(n-34) -10114987*a(n-35) +126407582*a(n-36) +102361211*a(n-37) -13113374*a(n-38) -92845724*a(n-39) -41282448*a(n-40) +19451206*a(n-41) +23428676*a(n-42) +5104632*a(n-43) -5396697*a(n-44) -2996014*a(n-45) +257192*a(n-46) +493476*a(n-47) +111556*a(n-48) -31808*a(n-49) -14768*a(n-50) +288*a(n-51) +384*a(n-52) for n>55

%e Some solutions for n=5

%e ..0..0..0..0. .0..0..0..0. .0..1..1..1. .0..0..1..1. .0..0..1..1

%e ..0..0..0..0. .1..0..0..1. .1..1..1..0. .1..0..1..0. .1..0..1..0

%e ..0..0..0..0. .1..1..0..1. .0..0..0..0. .1..1..1..0. .1..1..0..0

%e ..0..0..0..1. .0..0..0..0. .1..1..1..1. .0..0..1..0. .1..1..0..0

%e ..0..0..0..0. .0..1..0..0. .1..0..0..1. .1..0..1..1. .0..1..0..1

%Y Cf. A317697.

%K nonn

%O 1,1

%A _R. H. Hardin_, Aug 04 2018

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Last modified March 28 05:39 EDT 2024. Contains 371235 sequences. (Running on oeis4.)