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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.
11
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
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
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Jan 20 2017
STATUS
approved