A296804 T(n,k)=Number of nXk 0..1 arrays with each 1 adjacent to 1, 3 or 4 king-move neighboring 1s.

1, 2, 2, 3, 8, 3, 4, 15, 15, 4, 6, 41, 47, 41, 6, 9, 122, 164, 164, 122, 9, 13, 308, 694, 1011, 694, 308, 13, 19, 855, 2605, 6747, 6747, 2605, 855, 19, 28, 2405, 10149, 40956, 77705, 40956, 10149, 2405, 28, 41, 6522, 40768, 261107, 754400, 754400, 261107, 40768

Offset

1,2

Comments

Table starts

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

..2....8.....15.......41.......122.........308...........855............2405

..3...15.....47......164.......694........2605.........10149...........40768

..4...41....164.....1011......6747.......40956........261107.........1679397

..6..122....694.....6747.....77705......754400.......7978323........85842977

..9..308...2605....40956....754400....11910888.....203660310......3537017110

.13..855..10149...261107...7978323...203660310....5712715858....163079979478

.19.2405..40768..1679397..85842977..3537017110..163079979478...7684218661876

.28.6522.159911.10713116.905014451.60565369990.4582023008983.355189064928041

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) = a(n-1) +3*a(n-2) +9*a(n-3) -4*a(n-4) -12*a(n-5) -16*a(n-6)

k=3: [order 16]

k=4: [order 39]

Example

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

Crossrefs

Column 1 is A000930(n+1).

Sequence in context: A153216 A327259 A295943 * A296952 A141611 A234357

Adjacent sequences: A296801 A296802 A296803 * A296805 A296806 A296807

Keyword

nonn,tabl

Author

R. H. Hardin, Dec 20 2017

Status

approved