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A320402 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 2, 3 or 5 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero. 7
1, 2, 2, 4, 8, 4, 8, 28, 28, 8, 16, 97, 142, 97, 16, 32, 338, 732, 732, 338, 32, 64, 1178, 3694, 5956, 3694, 1178, 64, 128, 4105, 18754, 46516, 46516, 18754, 4105, 128, 256, 14305, 94842, 368049, 561290, 368049, 94842, 14305, 256, 512, 49850, 480321 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Table starts

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

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

...4....28.....142.......732........3694........18754..........94842

...8....97.....732......5956.......46516.......368049........2908839

..16...338....3694.....46516......561290......6845143.......83509525

..32..1178...18754....368049.....6845143....127789964.....2392115850

..64..4105...94842...2908839....83509525...2392115850....69104597430

.128.14305..480321..22987303..1016183713..44629532699..1987324601389

.256.49850.2431390.181744907.12380173295.834140753692.57271367516963

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..219

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 12] for n>14

k=4: [order 40] for n>41

EXAMPLE

Some solutions for n=5 k=4

..0..0..1..1. .0..1..0..0. .0..0..1..1. .0..0..0..0. .0..0..1..0

..0..0..0..0. .1..0..0..1. .1..1..0..0. .1..0..0..1. .0..1..1..1

..1..1..0..0. .0..0..1..1. .1..0..0..1. .1..0..1..0. .1..1..0..1

..0..0..0..0. .0..1..1..1. .1..0..0..1. .1..0..0..0. .1..1..0..1

..0..0..0..0. .1..0..0..0. .1..1..0..1. .1..0..0..1. .0..1..1..0

CROSSREFS

Column 1 is A000079(n-1).

Column 2 is A318010.

Sequence in context: A299753 A300267 A318016 * A208709 A300472 A326105

Adjacent sequences:  A320399 A320400 A320401 * A320403 A320404 A320405

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Oct 12 2018

STATUS

approved

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Last modified January 26 16:03 EST 2022. Contains 350599 sequences. (Running on oeis4.)