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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. 7
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 (list; table; graph; refs; listen; history; text; internal format)
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

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Last modified August 20 01:14 EDT 2019. Contains 326136 sequences. (Running on oeis4.)