A298770 T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 2, 3, 5 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, 957, 808, 604, 8, 13, 2048, 3124, 4288, 4288, 3124, 2048, 13, 21, 6948, 11807, 19722, 23932, 19722, 11807, 6948, 21, 34, 23652, 44846, 89295, 135243, 135243, 89295, 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.....957.....4288.....19722......89295......406426......1851746

..3...174....808....4288....23932....135243.....754713.....4245549.....23848195

..5...604...3124...19722...135243....942727....6456802....44530673....307427453

..8..2048..11807...89295...754713...6456802...53950338...454801194...3847185453

.13..6948..44846..406426..4245549..44530673..454801194..4698205702..48730992802

.21.23652.170350.1851746.23848195.307427453.3847185453.48730992802.620363350692

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 66] for n>69

Example

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

Crossrefs

Column 1 is A000045(n-1).

Column 2 is A297945.

Sequence in context: A298560 A298389 A299307 * A299567 A299465 A300108

Adjacent sequences: A298767 A298768 A298769 * A298771 A298772 A298773

Keyword

nonn,tabl

Author

R. H. Hardin, Jan 26 2018

Status

approved