A318016 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 2 or 3 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.

1, 2, 2, 4, 8, 4, 8, 28, 28, 8, 16, 97, 118, 97, 16, 32, 338, 508, 508, 338, 32, 64, 1178, 2130, 3062, 2130, 1178, 64, 128, 4105, 8971, 17703, 17703, 8971, 4105, 128, 256, 14305, 37700, 103633, 133136, 103633, 37700, 14305, 256, 512, 49850, 158613

Offset

1,2

Comments

Table starts

...1.....2......4........8........16..........32...........64...........128

...2.....8.....28.......97.......338........1178.........4105.........14305

...4....28....118......508......2130........8971........37700........158613

...8....97....508.....3062.....17703......103633.......603215.......3512154

..16...338...2130....17703....133136.....1033121......7960400......61442813

..32..1178...8971...103633...1033121....10674882....109443619....1125607630

..64..4105..37700...603215...7960400...109443619...1493271874...20443576030

.128.14305.158613..3512154..61442813..1125607630..20443576030..372575745070

.256.49850.667178.20446744.473867122.11570430384.279709797313.6788774522485

Links

R. H. Hardin, Table of n, a(n) for n = 1..312

Formula

Empirical for column k:

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

k=2: a(n) = 4*a(n-1) -2*a(n-2) +a(n-3) -a(n-4)

k=3: [order 11] for n>14

k=4: [order 26] for n>29

k=5: [order 61] for n>65

Example

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

Crossrefs

Column 1 is A000079(n-1).

Sequence in context: A299675 A299753 A300267 * A320402 A208709 A300472

Adjacent sequences: A318013 A318014 A318015 * A318017 A318018 A318019

Keyword

nonn,tabl

Author

R. H. Hardin, Aug 12 2018

Status

approved