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A317525 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 2, 3, 4, 5, 6 or 8 king-move adjacent elements, with upper left element zero. 7

%I #4 Jul 30 2018 11:40:25

%S 1,2,2,4,8,4,8,32,32,8,16,128,248,128,16,32,512,1921,1921,512,32,64,

%T 2048,14892,28760,14892,2048,64,128,8192,115446,431529,431529,115446,

%U 8192,128,256,32768,894961,6475106,12547746,6475106,894961,32768,256,512,131072

%N T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 2, 3, 4, 5, 6 or 8 king-move adjacent elements, with upper left element zero.

%C Table starts

%C ...1......2........4...........8............16...............32

%C ...2......8.......32.........128...........512.............2048

%C ...4.....32......248........1921.........14892...........115446

%C ...8....128.....1921.......28760........431529..........6475106

%C ..16....512....14892......431529......12547746........364882328

%C ..32...2048...115446.....6475106.....364882328......20564214798

%C ..64...8192...894961....97158833...10610584063....1158965686460

%C .128..32768..6937925..1457871738..308552557709...65318143510572

%C .256.131072.53784248.21875422403.8972619323210.3681268128789010

%H R. H. Hardin, <a href="/A317525/b317525.txt">Table of n, a(n) for n = 1..220</a>

%F Empirical for column k:

%F k=1: a(n) = 2*a(n-1)

%F k=2: a(n) = 4*a(n-1)

%F k=3: a(n) = 8*a(n-1) -2*a(n-2) +a(n-3) -3*a(n-4)

%F k=4: a(n) = 15*a(n-1) +a(n-2) -8*a(n-3) -84*a(n-4) -63*a(n-5) +24*a(n-6) +20*a(n-7)

%F k=5: [order 22]

%F k=6: [order 59]

%e Some solutions for n=5 k=4

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

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

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

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

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

%Y Column 1 is A000079(n-1).

%Y Column 2 is A004171(n-1).

%K nonn,tabl

%O 1,2

%A _R. H. Hardin_, Jul 30 2018

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Last modified March 28 09:04 EDT 2024. Contains 371240 sequences. (Running on oeis4.)