A274895 T(n,k)=Number of nXk 0..2 arrays with no element equal to any value at offset (0,-1) (-1,-1) or (-2,0) and new values introduced in order 0..2.

1, 1, 2, 2, 4, 3, 4, 12, 7, 6, 8, 36, 16, 14, 12, 16, 108, 37, 38, 26, 24, 32, 324, 86, 104, 84, 50, 48, 64, 972, 200, 290, 275, 192, 95, 96, 128, 2916, 465, 815, 913, 753, 436, 181, 192, 256, 8748, 1081, 2291, 3064, 3017, 2049, 990, 345, 384, 512, 26244, 2513, 6434, 10337

Offset: 1

Author

R. H. Hardin, Jul 10 2016

Keywords

• nonn
• tabl

Comments

Table starts

...1...1....2.....4......8......16.......32........64........128.........256

...2...4...12....36....108.....324......972......2916.......8748.......26244

...3...7...16....37.....86.....200......465......1081.......2513........5842

...6..14...38...104....290.....815.....2291......6434......18065.......50729

..12..26...84...275....913....3064....10337.....34921.....117975......398560

..24..50..192...753...3017...12217....49697....202749.....828828.....3391310

..48..95..436..2049...9863...48269...237807...1173787....5803040....28746995

..96.181..990..5602..32539..191974..1143185...6843349...41072451...246859250

.192.345.2253.15305.107369..767905..5539989..40156061..292253909..2133745005

.384.657.5121.41866.354366.3065418.26833885.236220817.2086382703.18485204565

Examples

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

Links

• R. H. Hardin, Table of n, a(n) for n = 1..420

Crossrefs

Column 1 is A003945(n-2).

Column 2 is A052535(n+1).

Row 1 is A000079(n-2).

Row 2 is A003946(n-1).

Row 3 is A010912(n-1).

Formula

Empirical for column k:

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

k=2: a(n) = a(n-1) +2*a(n-2) -a(n-4) for n>5

k=3: a(n) = a(n-1) +4*a(n-2) -6*a(n-4) -a(n-5) +4*a(n-6) -a(n-8) for n>10

k=4: [order 16] for n>18

k=5: [order 32] for n>34

k=6: [order 64] for n>66

Empirical for row n:

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

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

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

n=4: a(n) = 5*a(n-1) -9*a(n-2) +10*a(n-3) -6*a(n-4) +a(n-5) for n>6

n=5: [order 8] for n>9

n=6: [order 13] for n>14

n=7: [order 21] for n>22