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A280313
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 two elements, and with new values introduced in order 0 sequentially upwards.
5
0, 0, 0, 0, 0, 0, 1, 15, 15, 1, 2, 222, 788, 222, 2, 9, 2348, 20274, 20274, 2348, 9, 34, 21302, 415198, 1047790, 415198, 21302, 34, 124, 176125, 7506237, 43973846, 43973846, 7506237, 176125, 124, 432, 1370378, 125467047, 1638451216, 3802506340
OFFSET
1,8
COMMENTS
Table starts
....0........0............0..............1................2................9
....0........0...........15............222.............2348............21302
....0.......15..........788..........20274...........415198..........7506237
....1......222........20274........1047790.........43973846.......1638451216
....2.....2348.......415198.......43973846.......3802506340.....292789164101
....9....21302......7506237.....1638451216.....292789164101...46670265882656
...34...176125....125467047....56602534187...20928606452792.6910403433332994
..124..1370378...1986983748..1855013487412.1420117779715304
..432.10206549..30245976536.58477471703834
.1464.73563740.446674283782
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = 6*a(n-1) -6*a(n-2) -16*a(n-3) +12*a(n-4) +24*a(n-5) +8*a(n-6) for n>10
k=2: [order 12]
k=3: [order 36] for n>38
EXAMPLE
Some solutions for n=3 k=4
..0..0..1..2. .0..1..2..1. .0..0..1..1. .0..1..0..2. .0..0..0..1
..1..0..2..0. .2..1..2..0. .2..0..2..2. .1..1..0..1. .2..2..2..1
..2..0..2..0. .0..2..2..2. .2..2..1..0. .0..2..0..1. .1..1..0..0
CROSSREFS
Column 2 is A279530.
Sequence in context: A048294 A248391 A201345 * A291369 A069785 A290850
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Dec 31 2016
STATUS
approved