A304697 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 1, 2, 3, 5 or 6 king-move adjacent elements, with upper left element zero.

0, 1, 1, 1, 7, 1, 2, 16, 16, 2, 3, 45, 56, 45, 3, 5, 120, 178, 178, 120, 5, 8, 333, 669, 918, 669, 333, 8, 13, 928, 2615, 4910, 4910, 2615, 928, 13, 21, 2613, 9573, 24408, 37050, 24408, 9573, 2613, 21, 34, 7400, 35581, 124399, 263381, 263381, 124399, 35581, 7400

Offset

1,5

Comments

Table starts

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

..1....7.....16......45......120........333.........928..........2613

..1...16.....56.....178......669.......2615........9573.........35581

..2...45....178.....918.....4910......24408......124399........641663

..3..120....669....4910....37050.....263381.....1894297......13791026

..5..333...2615...24408...263381....2753404....27769991.....285425506

..8..928...9573..124399..1894297...27769991...389403912....5581948043

.13.2613..35581..641663.13791026..285425506..5581948043..111681916203

.21.7400.133149.3271834.99838011.2949991545.80739890302.2269676763262

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) = 2*a(n-1) +5*a(n-2) -2*a(n-3) -12*a(n-4) -8*a(n-5) for n>6

k=3: [order 19] for n>21

k=4: [order 69] for n>71

Example

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

Crossrefs

Column 1 is A000045(n-1).

Column 2 is A304013.

Sequence in context: A305367 A304959 A316641 * A316448 A316130 A317436

Adjacent sequences: A304694 A304695 A304696 * A304698 A304699 A304700

Keyword

nonn,tabl

Author

R. H. Hardin, May 17 2018

Status

approved