A317896 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 2, 3 or 4 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.

0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 2, 4, 2, 0, 0, 5, 13, 13, 5, 0, 0, 16, 59, 82, 59, 16, 0, 0, 45, 252, 549, 549, 252, 45, 0, 0, 123, 1074, 3697, 6193, 3697, 1074, 123, 0, 0, 340, 4633, 25169, 67792, 67792, 25169, 4633, 340, 0, 0, 946, 19933, 170608, 741031, 1184196, 741031

Offset

1,12

Comments

Table starts

.0...0.....0.......0........0..........0............0..............0

.0...1.....1.......2........5.........16...........45............123

.0...1.....4......13.......59........252.........1074...........4633

.0...2....13......82......549.......3697........25169.........170608

.0...5....59.....549.....6193......67792.......741031........8119416

.0..16...252....3697....67792....1184196.....20734591......364026326

.0..45..1074...25169...741031...20734591....580702029....16327953218

.0.123..4633..170608..8119416..364026326..16327953218...736219004144

.0.340.19933.1156219.88900423.6382316173.458323749120.33124631682770

Links

R. H. Hardin, Table of n, a(n) for n = 1..220

Formula

Empirical for column k:

k=1: a(n) = a(n-1)

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

k=3: [order 16] for n>18

k=4: [order 54] for n>56

Example

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

Crossrefs

Sequence in context: A011168 A058672 A278215 * A320364 A318222 A209466

Adjacent sequences: A317893 A317894 A317895 * A317897 A317898 A317899

Keyword

nonn,tabl

Author

R. H. Hardin, Aug 10 2018

Status

approved