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 A301330 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 2, 3, 5 or 6 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero. 7

%I #4 Mar 18 2018 08:41:41

%S 1,1,1,1,3,1,1,2,2,1,1,10,7,10,1,1,13,18,18,13,1,1,42,25,45,25,42,1,1,

%T 74,89,143,143,89,74,1,1,188,233,414,664,414,233,188,1,1,387,552,1481,

%U 2520,2520,1481,552,387,1,1,885,1559,5062,12342,17491,12342,5062,1559,885,1,1

%N T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 2, 3, 5 or 6 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....7....18.....25......89......233........552........1559.........4206

%C .1..10...18....45....143.....414.....1481.......5062.......17879........62112

%C .1..13...25...143....664....2520....12342......59524......283455......1368684

%C .1..42...89...414...2520...17491...116017.....770874.....5227338.....35859578

%C .1..74..233..1481..12342..116017..1127238...10358770....99285038....951443834

%C .1.188..552..5062..59524..770874.10358770..135428462..1814828567..24270760178

%C .1.387.1559.17879.283455.5227338.99285038.1814828567.34057380439.641360375141

%H R. H. Hardin, <a href="/A301330/b301330.txt">Table of n, a(n) for n = 1..219</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 28] for n>29

%e Some solutions for n=5 k=4

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

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

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

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

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

%Y Column 2 is A300374.

%K nonn,tabl

%O 1,5

%A _R. H. Hardin_, Mar 18 2018

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Last modified September 23 09:30 EDT 2023. Contains 365544 sequences. (Running on oeis4.)