A305961 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 1, 2, 3, 4, 5 or 7 king-move adjacent elements, with upper left element zero.

0, 1, 1, 1, 7, 1, 2, 25, 25, 2, 3, 98, 132, 98, 3, 5, 383, 919, 919, 383, 5, 8, 1493, 6030, 11142, 6030, 1493, 8, 13, 5824, 39985, 129452, 129452, 39985, 5824, 13, 21, 22717, 264680, 1510278, 2617757, 1510278, 264680, 22717, 21, 34, 88609, 1752681

Offset

1,5

Comments

Table starts

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

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

..1....25......132........919.........6030..........39985............264680

..2....98......919......11142.......129452........1510278..........17617201

..3...383.....6030.....129452......2617757.......53422574........1088558635

..5..1493....39985....1510278.....53422574.....1909062568.......68109190612

..8..5824...264680...17617201...1088558635....68109190612.....4251930563544

.13.22717..1752681..205511593..22189910134..2430866826404...265585355341963

.21.88609.11604776.2397335154.452276452312.86749580967244.16586555684575766

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 28] for n>29

Example

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

Crossrefs

Column 1 is A000045(n-1).

Column 2 is A304421.

Sequence in context: A317376 A304427 A316282 * A317222 A305692 A317072

Adjacent sequences: A305958 A305959 A305960 * A305962 A305963 A305964

Keyword

nonn,tabl

Author

R. H. Hardin, Jun 15 2018

Status

approved