A232920 T(n,k)=Number of nXk 0..2 arrays with no element x(i,j) adjacent to value 2-x(i,j) horizontally, diagonally or antidiagonally

3, 6, 9, 12, 18, 27, 24, 54, 54, 81, 48, 144, 246, 162, 243, 96, 396, 912, 1122, 486, 729, 192, 1080, 3612, 5808, 5118, 1458, 2187, 384, 2952, 13992, 33702, 37008, 23346, 4374, 6561, 768, 8064, 54600, 186720, 316800, 235824, 106494, 13122, 19683, 1536, 22032

Offset

1,1

Comments

Table starts

.....3......6.......12........24..........48............96............192

.....9.....18.......54.......144.........396..........1080...........2952

....27.....54......246.......912........3612.........13992..........54600

....81....162.....1122......5808.......33702........186720........1054446

...243....486.....5118.....37008......316800.......2515716.......20706696

...729...1458....23346....235824.....2986152......33994188......409408542

..2187...4374...106494...1502736....28178262.....459797904.....8119777890

..6561..13122...485778...9575856...266016264....6221092260...161274860934

.19683..39366..2215902..61020048..2511769872...84180552504..3205524631536

.59049.118098.10107954.388836912.23718269934.1139126465856.63736076920680

Links

R. H. Hardin, Table of n, a(n) for n = 1..391

Formula

Empirical for column k:

k=1: a(n) = 3*a(n-1)

k=2: a(n) = 3*a(n-1)

k=3: a(n) = 5*a(n-1) -2*a(n-2)

k=4: a(n) = 7*a(n-1) -4*a(n-2)

k=5: a(n) = 14*a(n-1) -45*a(n-2) +15*a(n-3) +36*a(n-4) -19*a(n-5) +2*a(n-6)

k=6: [order 9]

k=7: [order 19]

Empirical for row n:

n=1: a(n) = 2*a(n-1)

n=2: a(n) = 2*a(n-1) +2*a(n-2)

n=3: a(n) = 3*a(n-1) +4*a(n-2) -2*a(n-3) for n>4

n=4: a(n) = 3*a(n-1) +16*a(n-2) -3*a(n-3) -25*a(n-4) +2*a(n-5) +4*a(n-6) for n>7

n=5: [order 10] for n>11

n=6: [order 23] for n>24

n=7: [order 46] for n>47

Example

Some solutions for n=4 k=4
..0..0..1..0....0..0..1..0....0..0..1..0....0..0..1..0....1..0..0..1
..0..0..1..2....0..0..1..2....1..0..1..0....1..0..1..0....1..0..0..1
..1..0..1..2....0..0..1..0....1..0..1..2....0..0..1..2....0..0..0..0
..0..0..1..2....0..0..0..0....0..0..1..0....1..0..1..2....1..0..1..0

Crossrefs

Column 1 is A000244

Column 2 is A008776

Column 3 is A206144(n-1) for n>2

Column 4 is A223373

Row 1 is A003945

Sequence in context: A293396 A173195 A354785 * A092421 A109657 A175589

Adjacent sequences: A232917 A232918 A232919 * A232921 A232922 A232923

Keyword

nonn,tabl

Author

R. H. Hardin, Dec 02 2013

Status

approved