A297951 T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 2, 3 or 5 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, 948, 796, 604, 8, 13, 2048, 3079, 4258, 4258, 3079, 2048, 13, 21, 6948, 11614, 19561, 23840, 19561, 11614, 6948, 21, 34, 23652, 44076, 88441, 134642, 134642, 88441, 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.....948.....4258.....19561......88441......402245......1831311

..3...174....796....4258....23840....134642.....750733.....4222383.....23711537

..5...604...3079...19561...134642....938557....6423236....44289957....305715877

..8..2048..11614...88441...750733...6423236...53630550...451993176...3822668362

.13..6948..44076..402245..4222383..44289957..451993176..4667940027..48407285130

.21.23652.167210.1831311.23711537.305715877.3822668362.48407285130.616122541550

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 66] for n>69

Example

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

Crossrefs

Column 1 is A000045(n-1).

Sequence in context: A299228 A300040 A206359 * A298560 A298389 A299307

Adjacent sequences: A297948 A297949 A297950 * A297952 A297953 A297954

Keyword

nonn,tabl

Author

R. H. Hardin, Jan 09 2018

Status

approved