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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. 8
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 (list; table; graph; refs; listen; history; text; internal format)
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

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Last modified May 28 04:00 EDT 2020. Contains 334671 sequences. (Running on oeis4.)