A281540 - OEIS

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A281540

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

0, 0, 0, 0, 0, 0, 1, 4, 4, 1, 2, 104, 290, 104, 2, 9, 612, 2919, 2919, 612, 9, 34, 3056, 14561, 15624, 14561, 3056, 34, 124, 16368, 63840, 52529, 52529, 63840, 16368, 124, 432, 82656, 245037, 146956, 130646, 146956, 245037, 82656, 432, 1464, 397040, 871492

(list; table; graph; refs; listen; history; text; internal format)

OFFSET

1,8

COMMENTS

Table starts

....0.......0.......0.......1.......2.......9.......34......124......432

....0.......0.......4.....104.....612....3056....16368....82656...397040

....0.......4.....290....2919...14561...63840...245037...871492..2953605

....1.....104....2919...15624...52529..146956...385284...979866..2440042

....2.....612...14561...52529..130646..290073...610493..1274531..2667156

....9....3056...63840..146956..290073..560972..1066920..2001002..3797780

...34...16368..245037..385284..610493.1066920..1935368..3474958..6171868

..124...82656..871492..979866.1274531.2001002..3474958..6195904.10767665

..432..397040.2953605.2440042.2667156.3797780..6171868.10767665.18777294

.1464.1873344.9666482.5946178.5549073.7294930.11158871.18503172.31737730

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..241

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 22] for n>30

k=4: [order 36] for n>50

EXAMPLE

Some solutions for n=4 k=4

..0..1..0..1. .0..1..0..2. .0..1..0..1. .0..1..0..1. .0..0..1..0

..2..2..0..2. .2..2..1..2. .2..1..0..2. .2..1..2..2. .1..2..1..0

..1..1..1..1. .0..1..0..1. .0..0..2..1. .2..0..0..1. .0..0..2..0

..2..0..2..0. .0..2..2..2. .1..1..0..1. .1..2..2..1. .1..2..1..1

CROSSREFS

Column 1 is A280309.

Sequence in context: A225330 A094884 A359532 * A053216 A325489 A278516

Adjacent sequences: A281537 A281538 A281539 * A281541 A281542 A281543

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Jan 23 2017

STATUS

approved