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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
11
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
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 A375026 A109657
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Dec 02 2013
STATUS
approved