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

1,3

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

Links

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

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

Example

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

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).

Sequence in context: A223541 A128181 A125185 * A173387 A133438 A086671

Adjacent sequences: A274892 A274893 A274894 * A274896 A274897 A274898

Keyword

nonn,tabl

Author

R. H. Hardin, Jul 10 2016

Status

approved