A280284 T(n,k)=Number of nXk 0..2 arrays with no element equal to more than one of its horizontal and vertical neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.

0, 0, 0, 1, 4, 1, 2, 46, 46, 2, 8, 384, 996, 384, 8, 28, 2894, 16860, 16860, 2894, 28, 94, 20444, 259040, 592416, 259040, 20444, 94, 304, 138944, 3753846, 18844474, 18844474, 3753846, 138944, 304, 960, 918744, 52433492, 566131860, 1240628942

Offset

1,5

Comments

Table starts

....0........0............1..............2...............8...............28

....0........4...........46............384............2894............20444

....1.......46..........996..........16860..........259040..........3753846

....2......384........16860.........592416........18844474........566131860

....8.....2894.......259040.......18844474......1240628942......77217209188

...28....20444......3753846......566131860.....77217209188....9962925424456

...94...138944.....52433492....16393550046...4633270354464.1239330073038612

..304...918744....713549156...462579750172.270955366695864

..960..5954690...9525564453.12805032188772

.2976.38005496.125290653912

Links

R. H. Hardin, Table of n, a(n) for n = 1..84

Formula

Empirical for column k:

k=1: a(n) = 4*a(n-1) -8*a(n-3) -4*a(n-4) for n>7

k=2: [order 8]

k=3: [order 24] for n>25

Example

Some solutions for n=3 k=4
..0..1..0..2. .0..1..1..0. .0..0..1..2. .0..0..1..1. .0..1..2..0
..2..0..1..2. .2..0..2..0. .2..1..2..2. .1..0..2..0. .2..2..0..1
..2..0..0..1. .0..2..2..1. .0..2..1..1. .2..1..1..2. .0..1..0..0

Crossrefs

Column 2 is A279523.

Sequence in context: A299839 A265178 A159766 * A004161 A303141 A246070

Adjacent sequences: A280281 A280282 A280283 * A280285 A280286 A280287

Keyword

nonn,tabl

Author

R. H. Hardin, Dec 30 2016

Status

approved