A301354 T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 2, 3, 5 or 6 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.

0, 1, 1, 1, 3, 1, 2, 10, 10, 2, 3, 30, 53, 30, 3, 5, 96, 277, 277, 96, 5, 8, 307, 1433, 2349, 1433, 307, 8, 13, 981, 7522, 19561, 19561, 7522, 981, 13, 21, 3137, 39390, 165010, 264054, 165010, 39390, 3137, 21, 34, 10034, 206370, 1392131, 3579171, 3579171

Offset

1,5

Comments

Table starts

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

..1.....3......10.......30.........96..........307............981

..1....10......53......277.......1433.........7522..........39390

..2....30.....277.....2349......19561.......165010........1392131

..3....96....1433....19561.....264054......3579171.......48476633

..5...307....7522...165010....3579171.....78012336.....1702789144

..8...981...39390..1392131...48476633...1702789144....59990521481

.13..3137..206370.11741731..656551657..37169645074..2112136719464

.21.10034.1081141.99032014.8891966361.811102103620.74331048515102

Links

R. H. Hardin, Table of n, a(n) for n = 1..199

Formula

Empirical for column k:

k=1: a(n) = a(n-1) +a(n-2)

k=2: a(n) = 3*a(n-1) +a(n-2) -3*a(n-4) -2*a(n-5) -a(n-6) for n>7

k=3: [order 18] for n>20

k=4: [order 72] for n>73

Example

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

Crossrefs

Column 1 is A000045(n-1).

Column 2 is A300421.

Sequence in context: A300427 A300689 A300612 * A229187 A126226 A307665

Adjacent sequences: A301351 A301352 A301353 * A301355 A301356 A301357

Keyword

nonn,tabl

Author

R. H. Hardin, Mar 19 2018

Status

approved