A305452 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 1, 2, 4, 5 or 8 king-move adjacent elements, with upper left element zero.

0, 1, 1, 1, 3, 1, 2, 11, 11, 2, 3, 10, 7, 10, 3, 5, 51, 20, 20, 51, 5, 8, 165, 44, 26, 44, 165, 8, 13, 306, 77, 169, 169, 77, 306, 13, 21, 993, 181, 475, 1275, 475, 181, 993, 21, 34, 2867, 379, 1234, 2697, 2697, 1234, 379, 2867, 34, 55, 6818, 849, 5007, 13128, 5443, 13128

Offset

1,5

Comments

Table starts

..0....1...1.....2......3......5.......8.......13........21.........34

..1....3..11....10.....51....165.....306......993......2867.......6818

..1...11...7....20.....44.....77.....181......379.......849.......1799

..2...10..20....26....169....475....1234.....5007.....16422......51196

..3...51..44...169...1275...2697...13128....58608....222877.....971263

..5..165..77...475...2697...5443...30344...132479....485885....2234246

..8..306.181..1234..13128..30344..222961..1378090...6504099...42968149

.13..993.379..5007..58608.132479.1378090.10709608..62295992..516604339

.21.2867.849.16422.222877.485885.6504099.62295992.362139243.3817890104

Links

R. H. Hardin, Table of n, a(n) for n = 1..220

Formula

Empirical for column k:

k=1: a(n) = a(n-1) +a(n-2)

k=2: a(n) = a(n-1) +3*a(n-2) +8*a(n-3) -4*a(n-4) -16*a(n-5) for n>6

k=3: [order 17] for n>18

k=4: [order 63] for n>65

Example

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

Crossrefs

Column 1 is A000045(n-1).

Column 2 is A304052.

Sequence in context: A331692 A016567 A304058 * A304704 A316455 A305015

Adjacent sequences: A305449 A305450 A305451 * A305453 A305454 A305455

Keyword

nonn,tabl

Author

R. H. Hardin, Jun 01 2018

Status

approved