A298280 T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 2, 3, 4 or 5 king-move adjacent elements, with upper left element zero.

0, 1, 1, 1, 4, 1, 2, 18, 18, 2, 3, 64, 129, 64, 3, 5, 236, 873, 873, 236, 5, 8, 888, 6013, 10679, 6013, 888, 8, 13, 3336, 41437, 136006, 136006, 41437, 3336, 13, 21, 12512, 285280, 1735247, 3214459, 1735247, 285280, 12512, 21, 34, 46928, 1964290

Offset

1,5

Comments

Table starts

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

..1.....4.......18.........64...........236.............888..............3336

..1....18......129........873..........6013...........41437............285280

..2....64......873......10679........136006.........1735247..........22110710

..3...236.....6013.....136006.......3214459........75989207........1794078025

..5...888....41437....1735247......75989207......3328434344......145597697355

..8..3336...285280...22110710....1794078025....145597697355....11799327975543

.13.12512..1964290..281745241...42359577845...6369396379414...956310372633436

.21.46928.13524686.3590209542.1000164240246.278645510729761.77508769959888329

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) +4*a(n-3) for n>4

k=3: [order 10] for n>11

k=4: [order 30] for n>32

k=5: [order 92] for n>96

Example

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

Crossrefs

Column 1 is A000045(n-1).

Column 2 is A231950(n-1).

Sequence in context: A299567 A299465 A300108 * A299142 A299373 A299937

Adjacent sequences: A298277 A298278 A298279 * A298281 A298282 A298283

Keyword

nonn,tabl

Author

R. H. Hardin, Jan 16 2018

Status

approved