A318098 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 1, 2, 3 or 5 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.

0, 1, 1, 1, 5, 1, 2, 16, 16, 2, 3, 50, 45, 50, 3, 5, 160, 220, 220, 160, 5, 8, 511, 795, 1563, 795, 511, 8, 13, 1634, 3310, 9193, 9193, 3310, 1634, 13, 21, 5226, 12774, 57744, 73788, 57744, 12774, 5226, 21, 34, 16716, 51298, 356786, 679923, 679923, 356786, 51298

Offset

1,5

Comments

Table starts

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

..1.....5.....16.......50.......160.........511.........1634...........5226

..1....16.....45......220.......795........3310........12774..........51298

..2....50....220.....1563......9193.......57744.......356786........2215533

..3...160....795.....9193.....73788......679923......5965933.......53097417

..5...511...3310....57744....679923.....8985801....114914085.....1478603982

..8..1634..12774...356786...5965933...114914085...2154127036....40412593332

.13..5226..51298..2215533..53097417..1478603982..40412593332..1097965368750

.21.16716.201637.13752047.470312224.19018066407.760353849044.29957208854824

Links

R. H. Hardin, Table of n, a(n) for n = 1..198

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)

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

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

Example

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

Crossrefs

Column 1 is A000045(n-1).

Column 2 is A317817.

Sequence in context: A197080 A317823 A318430 * A318068 A165449 A019114

Adjacent sequences: A318095 A318096 A318097 * A318099 A318100 A318101

Keyword

nonn,tabl

Author

R. H. Hardin, Aug 16 2018

Status

approved