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A317896 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 2, 3 or 4 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero. 8
0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 2, 4, 2, 0, 0, 5, 13, 13, 5, 0, 0, 16, 59, 82, 59, 16, 0, 0, 45, 252, 549, 549, 252, 45, 0, 0, 123, 1074, 3697, 6193, 3697, 1074, 123, 0, 0, 340, 4633, 25169, 67792, 67792, 25169, 4633, 340, 0, 0, 946, 19933, 170608, 741031, 1184196, 741031 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,12

COMMENTS

Table starts

.0...0.....0.......0........0..........0............0..............0

.0...1.....1.......2........5.........16...........45............123

.0...1.....4......13.......59........252.........1074...........4633

.0...2....13......82......549.......3697........25169.........170608

.0...5....59.....549.....6193......67792.......741031........8119416

.0..16...252....3697....67792....1184196.....20734591......364026326

.0..45..1074...25169...741031...20734591....580702029....16327953218

.0.123..4633..170608..8119416..364026326..16327953218...736219004144

.0.340.19933.1156219.88900423.6382316173.458323749120.33124631682770

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..220

FORMULA

Empirical for column k:

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

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

k=3: [order 16] for n>18

k=4: [order 54] for n>56

EXAMPLE

Some solutions for n=5 k=4

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

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

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

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

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

CROSSREFS

Sequence in context: A011168 A058672 A278215 * A320364 A318222 A209466

Adjacent sequences:  A317893 A317894 A317895 * A317897 A317898 A317899

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Aug 10 2018

STATUS

approved

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Last modified October 16 13:20 EDT 2019. Contains 328082 sequences. (Running on oeis4.)