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.

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

Author

R. H. Hardin, Apr 20 2014

Keywords

• nonn
• tabl

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

Examples

			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
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..144

Crossrefs

Column 1 is A007051(n-1)

Row 1 is A000079(n-2)

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