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A298461 T(n,k)=Number of nXk 0..1 arrays with every element equal to 2, 3, 4, 5 or 6 king-move adjacent elements, with upper left element zero. 7

%I #6 Jan 19 2018 08:56:56

%S 0,0,0,0,1,0,0,3,3,0,0,6,8,6,0,0,17,30,30,17,0,0,41,153,219,153,41,0,

%T 0,104,710,2013,2013,710,104,0,0,261,3490,17443,35980,17443,3490,261,

%U 0,0,655,17087,158594,603930,603930,158594,17087,655,0,0,1646,84008,1441287

%N T(n,k)=Number of nXk 0..1 arrays with every element equal to 2, 3, 4, 5 or 6 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.......30........153..........710............3490.............17087

%C .0...6....30......219.......2013........17443..........158594...........1441287

%C .0..17...153.....2013......35980.......603930........10408388.........179761398

%C .0..41...710....17443.....603930.....19100497.......628485305.......20637616811

%C .0.104..3490...158594...10408388....628485305.....39291988976.....2452094749578

%C .0.261.17087..1441287..179761398..20637616811...2452094749578...290849365371077

%C .0.655.84008.13145287.3109300283.679019933720.153330900615477.34561341191060912

%H R. H. Hardin, <a href="/A298461/b298461.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 37] for n>38

%e Some solutions for n=5 k=4

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

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

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

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

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

%Y Column 2 is A297972.

%K nonn,tabl

%O 1,8

%A _R. H. Hardin_, Jan 19 2018

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Last modified May 28 18:29 EDT 2024. Contains 372919 sequences. (Running on oeis4.)