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A283572 T(n,k)=Number of nXk 0..1 arrays with no 1 equal to more than one of its horizontal, diagonal and antidiagonal neighbors, with the exception of exactly one element. 13
0, 0, 0, 1, 4, 0, 2, 26, 16, 0, 5, 72, 169, 68, 0, 12, 282, 674, 1108, 256, 0, 26, 908, 4313, 6812, 6453, 924, 0, 56, 2832, 21186, 67892, 60802, 36038, 3232, 0, 118, 8856, 104464, 509952, 945100, 528436, 194173, 11044, 0, 244, 26750, 513458, 3890056, 10919674 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,5

COMMENTS

Table starts

.0......0........1..........2............5.............12...............26

.0......4.......26.........72..........282............908.............2832

.0.....16......169........674.........4313..........21186...........104464

.0.....68.....1108.......6812........67892.........509952..........3890056

.0....256.....6453......60802.......945100.......10919674........129527524

.0....924....36038.....528436.....12699250......226897932.......4173039716

.0...3232...194173....4441052....164714523.....4558585174.....129997769458

.0..11044..1021432...36589848...2089140956....89724600000....3965206666608

.0..37104..5275885..296555892..26034179747..1736716820366..118919078661476

.0.122984.26869458.2373574616.320066184088.33188681249924.3520469545329364

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..241

FORMULA

Empirical for column k:

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

k=2: a(n) = 4*a(n-1) +2*a(n-2) -12*a(n-3) -11*a(n-4) +4*a(n-5) +6*a(n-6) -a(n-8)

k=3: [order 12]

k=4: [order 16]

k=5: [order 42]

k=6: [order 54]

Empirical for row n:

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

n=2: a(n) = 2*a(n-1) +5*a(n-2) +2*a(n-3) -17*a(n-4) -24*a(n-5) -16*a(n-6)

n=3: [order 12]

n=4: [order 16]

n=5: [order 42]

n=6: [order 64]

EXAMPLE

Some solutions for n=4 k=4

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

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

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

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

CROSSREFS

Column 2 is A283036.

Row 1 is A073778(n-1).

Sequence in context: A134895 A318468 A145877 * A057075 A281653 A327305

Adjacent sequences:  A283569 A283570 A283571 * A283573 A283574 A283575

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Mar 11 2017

STATUS

approved

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Last modified December 9 03:27 EST 2019. Contains 329872 sequences. (Running on oeis4.)