A295097 T(n,k)=Number of nXk 0..1 arrays with each 1 horizontally or vertically adjacent to 1 or 3 1s.

1, 2, 2, 3, 5, 3, 4, 11, 11, 4, 6, 24, 33, 24, 6, 9, 55, 114, 114, 55, 9, 13, 123, 377, 578, 377, 123, 13, 19, 276, 1249, 2859, 2859, 1249, 276, 19, 28, 621, 4151, 14187, 21185, 14187, 4151, 621, 28, 41, 1395, 13765, 70982, 158361, 158361, 70982, 13765, 1395, 41, 60

Offset

1,2

Comments

Table starts

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

..2....5....11......24.......55........123.........276...........621

..3...11....33.....114......377.......1249........4151.........13765

..4...24...114.....578.....2859......14187.......70982........353880

..6...55...377....2859....21185.....158361.....1182050.......8806229

..9..123..1249...14187...158361....1767431....19730839.....220211372

.13..276..4151...70982..1182050...19730839...329926211....5515740725

.19..621.13765..353880..8806229..220211372..5515740725..137994394960

.28.1395.45704.1763742.65681168.2459567704.92205260806.3452787904343

Links

R. H. Hardin, Table of n, a(n) for n = 1..287

Formula

Empirical for column k:

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

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

k=3: [order 16]

k=4: [order 45]

Example

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

Crossrefs

Column 1 is A000930(n+1).

Sequence in context: A285935 A209568 A227641 * A295551 A196696 A196729

Adjacent sequences: A295094 A295095 A295096 * A295098 A295099 A295100

Keyword

nonn,tabl

Author

R. H. Hardin, Nov 14 2017

Status

approved