A296952 T(n,k)=Number of nXk 0..1 arrays with each 1 adjacent to 1, 3 or 5 king-move neighboring 1s.

1, 2, 2, 3, 8, 3, 4, 16, 16, 4, 6, 36, 45, 36, 6, 9, 112, 135, 135, 112, 9, 13, 256, 544, 620, 544, 256, 13, 19, 608, 1765, 3637, 3637, 1765, 608, 19, 28, 1680, 5763, 17450, 37179, 17450, 5763, 1680, 28, 41, 4064, 20811, 86139, 256713, 256713, 86139, 20811, 4064

Offset

1,2

Comments

Table starts

..1....2.....3.......4.........6..........9...........13............19

..2....8....16......36.......112........256..........608..........1680

..3...16....45.....135.......544.......1765.........5763.........20811

..4...36...135.....620......3637......17450........86139........451210

..6..112...544....3637.....37179.....256713......1898178......16087936

..9..256..1765...17450....256713....2640993.....29067775.....356242817

.13..608..5763...86139...1898178...29067775....482228052....8786244680

.19.1680.20811..451210..16087936..356242817...8786244680..246430289779

.28.4064.70207.2267574.121741279.4007327435.148081034460.6194343019644

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) +a(n-3)

k=2: a(n) = 2*a(n-1) +8*a(n-3) -12*a(n-4)

k=3: [order 19]

k=4: [order 46]

Example

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

Crossrefs

Column 1 is A000930(n+1).

Sequence in context: A327259 A295943 A296804 * A141611 A234357 A145596

Adjacent sequences: A296949 A296950 A296951 * A296953 A296954 A296955

Keyword

nonn,tabl

Author

R. H. Hardin, Dec 22 2017

Status

approved