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A240893 T(n,k)=Number of nXk 0..2 arrays with no element equal to a different number of vertical neighbors than horizontal neighbors, with new values 0..2 introduced in row major order 7
1, 1, 1, 2, 4, 2, 4, 11, 11, 4, 8, 36, 57, 36, 8, 16, 116, 289, 289, 116, 16, 32, 376, 1485, 2362, 1485, 376, 32, 64, 1216, 7609, 19065, 19065, 7609, 1216, 64, 128, 3936, 38981, 154858, 245268, 154858, 38981, 3936, 128, 256, 12736, 199761, 1255585, 3146755 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

Table starts

...1.....1.......2.........4...........8.............16...............32

...1.....4......11........36.........116............376.............1216

...2....11......57.......289........1485...........7609............38981

...4....36.....289......2362.......19065.........154858..........1255585

...8...116....1485.....19065......245268........3146755.........40424861

..16...376....7609....154858.....3146755.......64074526.......1302610899

..32..1216...38981...1255585....40424861.....1302610899......41971040844

..64..3936..199761..10186158...519218802....26501432610....1352138182759

.128.12736.1023597..82615013..6669141957...539075345618...43565815810587

.256.41216.5245049.670126562.85661208693.10966382557858.1403705064843757

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..180

FORMULA

Empirical for column k:

k=1: a(n) = 2*a(n-1) for n>2

k=2: a(n) = 2*a(n-1) +4*a(n-2) for n>4

k=3: a(n) = 3*a(n-1) +8*a(n-2) +14*a(n-3) +4*a(n-4)

k=4: [order 16]

k=5: [order 48]

EXAMPLE

Some solutions for n=4 k=4

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

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

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

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

CROSSREFS

Column 1 is A000079(n-2)

Column 2 is A206687

Sequence in context: A298242 A282283 A288416 * A241108 A151706 A055372

Adjacent sequences:  A240890 A240891 A240892 * A240894 A240895 A240896

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Apr 14 2014

STATUS

approved

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Last modified November 28 13:30 EST 2021. Contains 349410 sequences. (Running on oeis4.)