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A302623 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 2 or 6 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero. 12
1, 2, 2, 4, 8, 4, 8, 17, 25, 8, 16, 37, 25, 81, 16, 32, 78, 45, 71, 264, 32, 64, 169, 79, 130, 191, 857, 64, 128, 361, 146, 251, 367, 498, 2785, 128, 256, 778, 286, 497, 896, 917, 1321, 9050, 256, 512, 1673, 563, 1051, 2229, 2669, 2533, 3505, 29407, 512, 1024, 3605 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Table starts

...1.....2....4.....8....16.....32......64......128.......256........512

...2.....8...17....37....78....169.....361......778......1673.......3605

...4....25...25....45....79....146.....286......563......1114.......2222

...8....81...71...130...251....497....1051.....2274......4999......10972

..16...264..191...367...896...2229....5771....15303.....41564.....113363

..32...857..498...917..2669...9015...30536...106951....390471....1418770

..64..2785.1321..2533..8283..36510..159831...722300...3485735...16654024

.128..9050.3505..6871.25770.150072..851266..5004858..32283797..204853561

.256.29407.9240.18334.79047.606756.4471550.34111427.294788397.2490596189

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..449

FORMULA

Empirical for column k:

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

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

k=3: [order 9] for n>11

k=4: [order 8] for n>10

k=5: [order 15] for n>20

k=6: [order 21] for n>27

k=7: [order 35] for n>43

Empirical for row n:

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

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

n=3: a(n) = 2*a(n-1) +a(n-3) -2*a(n-4) for n>8

n=4: [order 8] for n>11

n=5: [order 16] for n>21

n=6: [order 29] for n>35

n=7: [order 51] for n>62

EXAMPLE

Some solutions for n=5 k=4

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

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

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

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

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

CROSSREFS

Column 1 is A000079(n-1).

Column 2 is A240478.

Row 1 is A000079(n-1).

Row 2 is A281470.

Sequence in context: A183397 A339490 A281469 * A302415 A303182 A302322

Adjacent sequences:  A302620 A302621 A302622 * A302624 A302625 A302626

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Apr 10 2018

STATUS

approved

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Last modified October 23 04:06 EDT 2021. Contains 348211 sequences. (Running on oeis4.)