A299321 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 3, 4, 5, 6 or 7 king-move adjacent elements, with upper left element zero.

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 15, 2, 1, 1, 5, 10, 10, 5, 1, 1, 9, 70, 12, 70, 9, 1, 1, 22, 146, 130, 130, 146, 22, 1, 1, 45, 434, 284, 1306, 284, 434, 45, 1, 1, 101, 1206, 1557, 6051, 6051, 1557, 1206, 101, 1, 1, 218, 3228, 5838, 38035, 44381, 38035, 5838, 3228, 218, 1

Offset

1,12

Comments

Table starts

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

.1...1....1.....2.......5........9.........22...........45...........101

.1...1...15....10......70......146........434.........1206..........3228

.1...2...10....12.....130......284.......1557.........5838.........24821

.1...5...70...130....1306.....6051......38035.......234329.......1457212

.1...9..146...284....6051....44381.....473924......4898412......51303757

.1..22..434..1557...38035...473924....7885194....132676384....2249698337

.1..45.1206..5838..234329..4898412..132676384...3745566028..105240244212

.1.101.3228.24821.1457212.51303757.2249698337.105240244212.4909629881306

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-4) for n>5

k=3: [order 10] for n>12

k=4: [order 29] for n>30

Example

Some solutions for n=5 k=4
..0..0..0..1. .0..1..1..0. .0..0..0..0. .0..0..0..0. .0..1..1..0
..0..0..0..0. .1..1..1..1. .0..0..0..0. .0..0..0..0. .1..1..1..1
..1..1..0..0. .0..1..1..0. .1..0..1..0. .0..1..0..1. .0..1..1..1
..1..1..1..1. .1..1..1..1. .0..0..0..0. .0..0..0..0. .1..1..0..0
..0..1..1..1. .0..1..1..1. .0..0..0..0. .1..0..0..1. .1..1..0..0

Crossrefs

Column 2 is A052962(n-2).

Sequence in context: A193307 A331511 A201050 * A248537 A352000 A330073

Adjacent sequences: A299318 A299319 A299320 * A299322 A299323 A299324

Keyword

nonn,tabl

Author

R. H. Hardin, Feb 06 2018

Status

approved