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A283857 T(n,k)=Number of nXk 0..1 arrays with no 1 equal to more than three of its horizontal, diagonal and antidiagonal neighbors. 13
2, 4, 4, 8, 16, 8, 16, 61, 64, 16, 32, 233, 409, 256, 32, 64, 896, 2776, 2837, 1024, 64, 128, 3444, 19220, 35373, 19776, 4096, 128, 256, 13225, 131617, 456316, 448490, 137459, 16384, 256, 512, 50789, 901397, 5742620, 10741381, 5676420, 955680, 65536, 512 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Table starts

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

...4....16......61.......233..........896...........3444............13225

...8....64.....409......2776........19220.........131617...........901397

..16...256....2837.....35373.......456316........5742620.........72394838

..32..1024...19776....448490.....10741381......247708452.......5724272337

..64..4096..137459...5676420....252014450....10634931992.....449942735521

.128.16384..955680..71903903...5921518755...457711375590...35481195059121

.256.65536.6645662.910712188.139111379622.19691576356912.2796411775700471

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..221

FORMULA

Empirical for column k:

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

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

k=3: [order 8]

k=4: [order 17]

k=5: [order 45]

Empirical for row n:

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

n=2: a(n) = 3*a(n-1) +a(n-2) +7*a(n-3) +6*a(n-4)

n=3: [order 14]

n=4: [order 28]

n=5: [order 74]

EXAMPLE

Some solutions for n=4 k=4

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

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

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

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

CROSSREFS

Column 1 is A000079.

Column 2 is A000302.

Row 1 is A000079.

Sequence in context: A297374 A297102 A283415 * A227442 A282316 A228986

Adjacent sequences:  A283854 A283855 A283856 * A283858 A283859 A283860

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Mar 17 2017

STATUS

approved

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Last modified November 29 18:41 EST 2021. Contains 349416 sequences. (Running on oeis4.)