A275131 T(n,k)=Number of nXk 0..2 arrays with no element equal to any value at offset (-2,-2) (-1,0) or (-1,1) and new values introduced in order 0..2.

1, 2, 1, 5, 4, 2, 14, 16, 12, 4, 41, 64, 45, 36, 8, 122, 256, 174, 129, 108, 16, 365, 1024, 675, 568, 373, 324, 32, 1094, 4096, 2607, 2545, 2178, 1083, 972, 64, 3281, 16384, 10077, 11092, 12423, 8321, 3148, 2916, 128, 9842, 65536, 38967, 48451, 71576, 62378

Offset: 1

Author

R. H. Hardin, Jul 17 2016

Keywords

• nonn
• tabl

Comments

Table starts

...1.....2.....5......14.......41.......122.........365.........1094

...1.....4....16......64......256......1024........4096........16384

...2....12....45.....174......675......2607.......10077........38967

...4....36...129.....568.....2545.....11092.......48451.......212897

...8...108...373....2178....12423.....71576......412306......2381629

..16...324..1083....8321....62378....473185.....3586068.....27224209

..32...972..3148...31772...315021...3146574....31446544....315531602

..64..2916..9157..121707..1591442..20970214...276145917...3669759648

.128..8748.26623..466252..8024937.139845553..2432426709..42807577389

.256.26244.77372.1783920.40445177.930732169.21443562178.499213473864

Examples

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

Links

• R. H. Hardin, Table of n, a(n) for n = 1..312

Crossrefs

Column 1 is A000079(n-2).

Column 2 is A003946(n-1).

Row 1 is A007051(n-1).

Row 2 is A000302(n-1).

Formula

Empirical for column k:

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

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

k=3: [order 9] for n>10

k=4: [order 17] for n>20

k=5: [order 28] for n>31

k=6: [order 67] for n>70

Empirical for row n:

n=1: a(n) = 4*a(n-1) -3*a(n-2)

n=2: a(n) = 4*a(n-1)

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

n=4: [order 9] for n>11

n=5: [order 10] for n>14

n=6: [order 26] for n>28

n=7: [order 53] for n>58