A298560 T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 2, 3, 5 or 7 king-move adjacent elements, with upper left element zero.

0, 1, 1, 1, 4, 1, 2, 18, 18, 2, 3, 52, 56, 52, 3, 5, 174, 219, 219, 174, 5, 8, 604, 796, 956, 796, 604, 8, 13, 2048, 3079, 4304, 4304, 3079, 2048, 13, 21, 6948, 11614, 19843, 24364, 19843, 11614, 6948, 21, 34, 23652, 44076, 90153, 138774, 138774, 90153, 44076

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.....56.....219......796......3079......11614.......44076.......167210

..2....52....219.....956.....4304.....19843......90153......411915......1883419

..3...174....796....4304....24364....138774.....781071.....4432262.....25124403

..5...604...3079...19843...138774....983554....6852589....48019258....337105690

..8..2048..11614...90153...781071...6852589...58699120...506226692...4381689438

.13..6948..44076..411915..4432262..48019258..506226692..5376664548..57373679100

.21.23652.167210.1883419.25124403.337105690.4381689438.57373679100.755503324152

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 20] for n>21

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

Example

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

Crossrefs

Column 1 is A000045(n-1).

Column 2 is A297945.

Column 3 is A297946.

Sequence in context: A300040 A206359 A297951 * A298389 A299307 A298770

Adjacent sequences: A298557 A298558 A298559 * A298561 A298562 A298563

Keyword

nonn,tabl

Author

R. H. Hardin, Jan 21 2018

Status

approved