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A241370
T(n,k)=Number of nXk 0..2 arrays with no element equal to fewer vertical neighbors than horizontal neighbors, with new values 0..2 introduced in row major order
14
1, 1, 2, 2, 7, 5, 4, 28, 47, 14, 8, 121, 460, 326, 41, 16, 523, 4617, 7376, 2284, 122, 32, 2261, 46245, 169982, 118488, 16026, 365, 64, 9775, 463567, 3910194, 6280325, 1904096, 112458, 1094, 128, 42261, 4646421, 90008909, 332185927, 232173463
OFFSET
1,3
COMMENTS
Table starts
....1.......1..........2..............4.................8...................16
....2.......7.........28............121...............523.................2261
....5......47........460...........4617.............46245...............463567
...14.....326.......7376.........169982...........3910194.............90008909
...41....2284.....118488........6280325.........332185927..........17583615124
..122...16026....1904096......232173463.......28238828935........3437694358689
..365..112458...30598800.....8582759752.....2400505507498......672068364873884
.1094..789166..491723328...317280724429...204061855414167...131390467341043995
.3281.5537942.7902006144.11729003927933.17346886991310331.25687100469219790719
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = 4*a(n-1) -3*a(n-2)
k=2: a(n) = 7*a(n-1) +2*a(n-3) -8*a(n-4) for n>5
k=3: [order 8]
k=4: [order 31]
k=5: [order 94]
Empirical for row n:
n=1: a(n) = 2*a(n-1) for n>2
n=2: a(n) = 5*a(n-1) -2*a(n-2) -4*a(n-3) for n>5
n=3: a(n) = 9*a(n-1) +16*a(n-2) -50*a(n-3) -72*a(n-4) -32*a(n-5) -32*a(n-6) for n>8
n=4: [order 21] for n>23
n=5: [order 65] for n>67
EXAMPLE
Some solutions for n=4 k=4
..0..1..0..1....0..1..0..2....0..1..0..2....0..1..0..2....0..1..0..2
..1..1..2..0....1..0..2..1....0..2..0..0....2..0..0..1....0..1..2..1
..1..2..2..0....2..0..0..1....1..2..0..0....1..0..2..0....2..0..1..0
..1..2..2..1....0..1..0..2....0..1..0..1....2..0..1..2....1..0..1..0
CROSSREFS
Column 1 is A007051(n-1)
Row 1 is A000079(n-2)
Sequence in context: A325525 A309554 A011146 * A197735 A249493 A223000
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Apr 20 2014
STATUS
approved