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 A297978 T(n,k)=Number of nXk 0..1 arrays with every element equal to 2, 3, 4 or 5 king-move adjacent elements, with upper left element zero. 8

%I #4 Jan 10 2018 06:55:45

%S 0,0,0,0,1,0,0,3,3,0,0,6,8,6,0,0,17,20,20,17,0,0,41,124,109,124,41,0,

%T 0,104,501,1042,1042,501,104,0,0,261,2410,7302,18037,7302,2410,261,0,

%U 0,655,11304,60427,242401,242401,60427,11304,655,0,0,1646,53108,481401,3565760

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

%C Table starts

%C .0...0.....0.......0.........0............0..............0................0

%C .0...1.....3.......6........17...........41............104..............261

%C .0...3.....8......20.......124..........501...........2410............11304

%C .0...6....20.....109......1042.........7302..........60427...........481401

%C .0..17...124....1042.....18037.......242401........3565760.........52222182

%C .0..41...501....7302....242401......5902043......160132152.......4278426570

%C .0.104..2410...60427...3565760....160132152.....7833283900.....380347270776

%C .0.261.11304..481401..52222182...4278426570...380347270776...33544649054853

%C .0.655.53108.3880101.765460393.114579985316.18479502350618.2962364663254528

%H R. H. Hardin, <a href="/A297978/b297978.txt">Table of n, a(n) for n = 1..180</a>

%F Empirical for column k:

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

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

%F k=3: [order 13] for n>15

%F k=4: [order 46] for n>49

%e Some solutions for n=5 k=4

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

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

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

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

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

%K nonn,tabl

%O 1,8

%A _R. H. Hardin_, Jan 10 2018

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Last modified May 21 04:19 EDT 2024. Contains 372720 sequences. (Running on oeis4.)