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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.
6
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
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
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Dec 30 2016
STATUS
approved