A298622 - OEIS

A298622

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

0, 1, 1, 0, 4, 0, 1, 4, 4, 1, 0, 16, 0, 16, 0, 1, 48, 7, 7, 48, 1, 0, 88, 7, 83, 7, 88, 0, 1, 240, 25, 218, 218, 25, 240, 1, 0, 704, 88, 682, 1893, 682, 88, 704, 0, 1, 1600, 187, 4068, 5749, 5749, 4068, 187, 1600, 1, 0, 4032, 491, 14719, 51213, 32834, 51213, 14719, 491, 4032

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OFFSET

1,5

COMMENTS

Table starts

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

.1....4...4....16......48.......88........240.........704..........1600

.0....4...0.....7.......7.......25.........88.........187...........491

.1...16...7....83.....218......682.......4068.......14719.........58834

.0...48...7...218....1893.....5749......51213......407430.......2021867

.1...88..25...682....5749....32834.....480343.....4361690......38698593

.0..240..88..4068...51213...480343...10823065...161922923....2400592063

.1..704.187.14719..407430..4361690..161922923..4673855921...92707820639

.0.1600.491.58834.2021867.38698593.2400592063.92707820639.3376311711594

LINKS

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

FORMULA

Empirical for column k:

k=1: a(n) = a(n-2)

k=2: a(n) = 2*a(n-1) +8*a(n-3) -8*a(n-4) -8*a(n-5)

k=3: [order 19] for n>20

k=4: [order 64] for n>65

EXAMPLE

Some solutions for n=5 k=4

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

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

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

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

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

CROSSREFS

Column 2 is A298448.

Sequence in context: A309333 A298924 A217476 * A298454 A298834 A299588

Adjacent sequences: A298619 A298620 A298621 * A298623 A298624 A298625

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Jan 23 2018

STATUS

approved