A299567 T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 2, 3, 5, 7 or 8 king-move adjacent elements, with upper left element zero.

0, 1, 1, 1, 4, 1, 2, 18, 18, 2, 3, 52, 57, 52, 3, 5, 174, 222, 222, 174, 5, 8, 604, 808, 965, 808, 604, 8, 13, 2048, 3124, 4342, 4342, 3124, 2048, 13, 21, 6948, 11807, 20044, 24588, 20044, 11807, 6948, 21, 34, 23652, 44846, 91193, 140401, 140401, 91193, 44846

Offset

1,5

Comments

Table starts

..0.....1......1.......2........3.........5..........8..........13...........21

..1.....4.....18......52......174.......604.......2048........6948........23652

..1....18.....57.....222......808......3124......11807.......44846.......170350

..2....52....222.....965.....4342.....20044......91193......417122......1909312

..3...174....808....4342....24588....140401.....792454.....4505710.....25597272

..5...604...3124...20044...140401....997212....6974944....49037025....345316723

..8..2048..11807...91193...792454...6974944...60087975...521019836...4532637754

.13..6948..44846..417122..4505710..49037025..521019836..5576669621..59935963606

.21.23652.170350.1909312.25597272.345316723.4532637754.59935963606.796438022548

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) +a(n-2)

k=2: a(n) = 4*a(n-1) -2*a(n-2) +2*a(n-3) -6*a(n-4) -4*a(n-5) for n>6

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

k=4: [order 67] for n>70

Example

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

Crossrefs

Column 1 is A000045(n-1).

Column 2 is A297945.

Column 3 is A298765.

Sequence in context: A298389 A299307 A298770 * A299465 A300108 A298280

Adjacent sequences: A299564 A299565 A299566 * A299568 A299569 A299570

Keyword

nonn,tabl

Author

R. H. Hardin, Feb 12 2018

Status

approved