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A316921 Number of nX4 0..1 arrays with every element unequal to 0, 1, 3, 4, 5, 6 or 7 king-move adjacent elements, with upper left element zero. 1

%I

%S 5,21,31,137,594,2574,15118,95244,569635,3550989,22664602,142267931,

%T 895070740,5670787406,35824811579,226112280654,1429458076391,

%U 9034826810108,57079202265029,360713789484186,2279666370535566

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

%C Column 4 of A316925.

%H R. H. Hardin, <a href="/A316921/b316921.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 12*a(n-1) -51*a(n-2) +195*a(n-3) -1005*a(n-4) +2944*a(n-5) -5362*a(n-6) +17291*a(n-7) -47505*a(n-8) +74205*a(n-9) -168436*a(n-10) +362058*a(n-11) -413187*a(n-12) +663946*a(n-13) -969737*a(n-14) +420286*a(n-15) -481243*a(n-16) +147478*a(n-17) +1080505*a(n-18) -2336922*a(n-19) +6600322*a(n-20) -6551295*a(n-21) +4173168*a(n-22) -688068*a(n-23) +7432137*a(n-24) -12589162*a(n-25) -9372774*a(n-26) -10500723*a(n-27) +7447976*a(n-28) -25119541*a(n-29) +41488482*a(n-30) +73870327*a(n-31) +55330350*a(n-32) -120181727*a(n-33) -118352377*a(n-34) +7630520*a(n-35) +110429964*a(n-36) +53450039*a(n-37) -34148921*a(n-38) -41621802*a(n-39) -10964908*a(n-40) +11985455*a(n-41) +6354761*a(n-42) -2636376*a(n-43) -2126588*a(n-44) -231100*a(n-45) +594984*a(n-46) +139724*a(n-47) -101338*a(n-48) -11668*a(n-49) +9336*a(n-50) +1440*a(n-51) for n>55

%e Some solutions for n=5

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

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

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

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

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

%Y Cf. A316925.

%K nonn

%O 1,1

%A _R. H. Hardin_, Jul 16 2018

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Last modified May 17 06:27 EDT 2022. Contains 353730 sequences. (Running on oeis4.)