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 A296688 T(n,k)=Number of nXk 0..1 arrays with each 1 adjacent to 1, 2 or 3 king-move neighboring 1s. 8

%I #4 Dec 18 2017 12:10:37

%S 1,2,2,4,12,4,7,43,43,7,12,145,210,145,12,21,524,1162,1162,524,21,37,

%T 1888,6959,11478,6959,1888,37,65,6737,39608,121477,121477,39608,6737,

%U 65,114,24093,226599,1210458,2323514,1210458,226599,24093,114,200,86250

%N T(n,k)=Number of nXk 0..1 arrays with each 1 adjacent to 1, 2 or 3 king-move neighboring 1s.

%C Table starts

%C ...1.....2.......4..........7...........12.............21...............37

%C ...2....12......43........145..........524...........1888.............6737

%C ...4....43.....210.......1162.........6959..........39608...........226599

%C ...7...145....1162......11478.......121477........1210458.........12227803

%C ..12...524....6959.....121477......2323514.......40828110........732185986

%C ..21..1888...39608....1210458.....40828110.....1231267842......38342595769

%C ..37..6737..226599...12227803....732185986....38342595769....2094245366560

%C ..65.24093.1305725..124103052..13222385649..1202783176853..115207878553368

%C .114.86250.7497482.1254382781.237236541596.37385385800350.6267132000869767

%H R. H. Hardin, <a href="/A296688/b296688.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) -a(n-2) +a(n-3)

%F k=2: a(n) = 3*a(n-1) -a(n-2) +11*a(n-3) -2*a(n-4) +8*a(n-5) -4*a(n-6)

%F k=3: [order 12]

%F k=4: [order 26]

%F k=5: [order 63]

%e Some solutions for n=4 k=4

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

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

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

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

%Y Column 1 is A005251(n+2).

%K nonn,tabl

%O 1,2

%A _R. H. Hardin_, Dec 18 2017

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Last modified May 29 00:29 EDT 2024. Contains 372921 sequences. (Running on oeis4.)