A298382 - OEIS

A298382

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

1, 1, 1, 1, 5, 1, 1, 7, 7, 1, 1, 18, 6, 18, 1, 1, 31, 18, 18, 31, 1, 1, 65, 30, 47, 30, 65, 1, 1, 130, 87, 172, 172, 87, 130, 1, 1, 253, 200, 504, 852, 504, 200, 253, 1, 1, 519, 522, 1502, 3271, 3271, 1502, 522, 519, 1, 1, 1018, 1421, 5011, 12982, 17749, 12982, 5011, 1421

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OFFSET

1,5

COMMENTS

Table starts

.1...1....1.....1......1.......1........1.........1..........1............1

.1...5....7....18.....31......65......130.......253........519.........1018

.1...7....6....18.....30......87......200.......522.......1421.........3805

.1..18...18....47....172.....504.....1502......5011......16723........55130

.1..31...30...172....852....3271....12982.....61188.....269075......1128296

.1..65...87...504...3271...17749....94292....570906....3475015.....19883608

.1.130..200..1502..12982...94292...682833...5489368...43729967....338622211

.1.253..522..5011..61188..570906..5489368..59733814..631658087...6469036635

.1.519.1421.16723.269075.3475015.43729967.631658087.9025761348.123286546709

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..199

FORMULA

Empirical for column k:

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

k=2: a(n) = a(n-1) +3*a(n-2) -4*a(n-4) for n>5

k=3: [order 17] for n>18

k=4: [order 71] for n>72

EXAMPLE

Some solutions for n=6 k=4

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

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

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

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

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

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

CROSSREFS

Column 2 is A297937.

Sequence in context: A298554 A298727 A299561 * A299249 A299458 A300096

Adjacent sequences: A298379 A298380 A298381 * A298383 A298384 A298385

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Jan 18 2018

STATUS

approved