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 A300380 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 2 or 3 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero. 8

%I #4 Mar 04 2018 09:20:26

%S 1,1,1,1,3,1,1,2,2,1,1,10,4,10,1,1,13,11,11,13,1,1,42,8,26,8,42,1,1,

%T 74,58,80,80,58,74,1,1,188,131,237,389,237,131,188,1,1,387,306,692,

%U 1351,1351,692,306,387,1,1,885,936,2548,6577,8839,6577,2548,936,885,1,1,1937

%N T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 2 or 3 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.

%C Table starts

%C .1...1...1....1......1.......1........1.........1..........1............1

%C .1...3...2...10.....13......42.......74.......188........387..........885

%C .1...2...4...11......8......58......131.......306........936.........2435

%C .1..10..11...26.....80.....237......692......2548.......8240........26808

%C .1..13...8...80....389....1351.....6577.....29663.....128834.......599170

%C .1..42..58..237...1351....8839....53367....330577....2105279.....13511213

%C .1..74.131..692...6577...53367...481311...4070089...36505624....319929622

%C .1.188.306.2548..29663..330577..4070089..47968011..590197943...7181318177

%C .1.387.936.8240.128834.2105279.36505624.590197943.9905247305.168928472097

%H R. H. Hardin, <a href="/A300380/b300380.txt">Table of n, a(n) for n = 1..238</a>

%F Empirical for column k:

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

%F k=2: a(n) = 4*a(n-2) +2*a(n-3) +a(n-5) -3*a(n-6) +a(n-7)

%F k=3: [order 23] for n>25

%F k=4: [order 80] for n>82

%e Some solutions for n=5 k=4

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

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

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

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

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

%K nonn,tabl

%O 1,5

%A _R. H. Hardin_, Mar 04 2018

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Last modified December 7 18:28 EST 2023. Contains 367660 sequences. (Running on oeis4.)