A298629 - OEIS

A298629

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

0, 0, 0, 0, 1, 0, 0, 3, 3, 0, 0, 6, 8, 6, 0, 0, 17, 26, 26, 17, 0, 0, 41, 138, 125, 138, 41, 0, 0, 104, 611, 1218, 1218, 611, 104, 0, 0, 261, 2880, 8617, 20959, 8617, 2880, 261, 0, 0, 655, 13727, 71334, 285085, 285085, 71334, 13727, 655, 0, 0, 1646, 65070, 577595, 4228781

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OFFSET

1,8

COMMENTS

Table starts

.0...0.....0.......0.........0............0..............0................0

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

.0...3.....8......26.......138..........611...........2880............13727

.0...6....26.....125......1218.........8617..........71334...........577595

.0..17...138....1218.....20959.......285085........4228781.........62707643

.0..41...611....8617....285085......7087666......193309200.......5247911837

.0.104..2880...71334...4228781....193309200.....9557110072.....471778534219

.0.261.13727..577595..62707643...5247911837...471778534219...42384213387355

.0.655.65070.4700651.929296248.142315671147.23254989974319.3802910270886730

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..180

FORMULA

Empirical for column k:

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

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

k=3: [order 11] for n>12

k=4: [order 48]

EXAMPLE

Some solutions for n=5 k=4

..0..0..0..1. .0..0..0..0. .0..1..1..1. .0..0..0..0. .0..0..0..0

..0..0..1..1. .1..0..0..0. .0..0..1..1. .0..0..0..0. .0..1..1..0

..0..0..0..0. .1..1..0..0. .1..0..0..0. .0..1..0..0. .0..0..1..1

..1..1..0..1. .0..1..1..0. .1..1..0..0. .1..1..1..0. .0..0..0..1

..1..1..1..1. .0..0..1..1. .1..0..0..0. .1..1..0..0. .0..0..0..0

CROSSREFS

Column 2 is A297972.

Sequence in context: A335682 A335681 A297978 * A298461 A299334 A268759

Adjacent sequences: A298626 A298627 A298628 * A298630 A298631 A298632

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Jan 23 2018

STATUS

approved