A304704 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 1, 2, 4, 5 or 6 king-move adjacent elements, with upper left element zero.

0, 1, 1, 1, 3, 1, 2, 11, 11, 2, 3, 10, 8, 10, 3, 5, 51, 21, 21, 51, 5, 8, 165, 46, 48, 46, 165, 8, 13, 306, 103, 215, 215, 103, 306, 13, 21, 993, 201, 798, 908, 798, 201, 993, 21, 34, 2867, 512, 3055, 5232, 5232, 3055, 512, 2867, 34, 55, 6818, 1123, 9810, 19701, 47440, 19701

Offset

1,5

Comments

Table starts

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

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

..1...11....8....21.....46......103.......201.........512.........1123

..2...10...21....48....215......798......3055........9810........41744

..3...51...46...215....908.....5232.....19701......135455.......872954

..5..165..103...798...5232....47440....296646.....2733069.....26024851

..8..306..201..3055..19701...296646...3510334....37931518....611105804

.13..993..512..9810.135455..2733069..37931518...799135415..19924071081

.21.2867.1123.41744.872954.26024851.611105804.19924071081.758781064050

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) = 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>20

k=4: [order 67] for n>69

Example

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

Crossrefs

Column 1 is A000045(n-1).

Column 2 is A304052.

Sequence in context: A016567 A304058 A305452 * A316455 A305015 A316648

Adjacent sequences: A304701 A304702 A304703 * A304705 A304706 A304707

Keyword

nonn,tabl

Author

R. H. Hardin, May 17 2018

Status

approved