A316282 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 1, 2, 3, 4, 5 or 8 king-move adjacent elements, with upper left element zero.

0, 1, 1, 1, 7, 1, 2, 25, 25, 2, 3, 98, 125, 98, 3, 5, 383, 846, 846, 383, 5, 8, 1493, 5321, 9540, 5321, 1493, 8, 13, 5824, 34017, 102072, 102072, 34017, 5824, 13, 21, 22717, 216805, 1099200, 1820908, 1099200, 216805, 22717, 21, 34, 88609, 1382759

Offset

1,5

Comments

Table starts

..0.....1.......1..........2............3..............5................8

..1.....7......25.........98..........383...........1493.............5824

..1....25.....125........846.........5321..........34017...........216805

..2....98.....846.......9540.......102072........1099200.........11834419

..3...383....5321.....102072......1820908.......32932624........594230641

..5..1493...34017....1099200.....32932624.....1000914270......30350372014

..8..5824..216805...11834419....594230641....30350372014....1545539179382

.13.22717.1382759..127394654..10728510594...920820679433...78766985363848

.21.88609.8818011.1371525369.193678113501.27936246990475.4013958393240781

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) = 3*a(n-1) +3*a(n-2) +2*a(n-3)

k=3: [order 9] for n>10

k=4: [order 27] for n>28

k=5: [order 95] for n>97

Example

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

Crossrefs

Column 1 is A000045(n-1).

Column 2 is A304421.

Sequence in context: A306143 A317376 A304427 * A305961 A317222 A305692

Adjacent sequences: A316279 A316280 A316281 * A316283 A316284 A316285

Keyword

nonn,tabl

Author

R. H. Hardin, Jun 28 2018

Status

approved