A281326 T(n,k)=Number of nXk 0..2 arrays with no element equal to more than one of its horizontal and antidiagonal neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.

0, 0, 0, 1, 2, 0, 2, 46, 28, 0, 8, 394, 1266, 304, 0, 28, 3102, 21734, 27144, 2976, 0, 94, 22342, 350818, 953236, 521848, 27488, 0, 304, 153982, 5192104, 31906806, 37854870, 9439296, 244544, 0, 960, 1028164, 73653131, 977717308, 2628860468, 1420883314

Offset

1,5

Comments

Table starts

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

.0.........2...........46..............394..............3102..............22342

.0........28.........1266............21734............350818............5192104

.0.......304........27144...........953236..........31906806..........977717308

.0......2976.......521848.........37854870........2628860468.......166805996158

.0.....27488......9439296.......1420883314......204635003232.....26899223667928

.0....244544....164206368......51413566384....15351923549506...4181821443113978

.0...2119168...2780073856....1813061036754..1122266386967854.633606104886468360

.0..18011136..46137121152...62727044483806.80481356765998482

.0.150809088.754039756800.2138467742923228

Links

R. H. Hardin, Table of n, a(n) for n = 1..97

Formula

Empirical for column k:

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

k=2: a(n) = 16*a(n-1) -72*a(n-2) +64*a(n-3) -16*a(n-4)

k=3: a(n) = 28*a(n-1) -180*a(n-2) -224*a(n-3) -64*a(n-4) for n>5

k=4: [order 8] for n>9

k=5: [order 16] for n>18

Empirical for row n:

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

n=2: [order 10] for n>11

n=3: [order 36] for n>39

Example

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

Crossrefs

Row 1 is A280279.

Sequence in context: A093857 A056949 A346235 * A012622 A013370 A013374

Adjacent sequences: A281323 A281324 A281325 * A281327 A281328 A281329

Keyword

nonn,tabl

Author

R. H. Hardin, Jan 20 2017

Status

approved