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

1,2

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

Links

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

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

Example

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

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).

Sequence in context: A164678 A164679 A275183 * A280513 A185023 A372501

Adjacent sequences: A275128 A275129 A275130 * A275132 A275133 A275134

Keyword

nonn,tabl

Author

R. H. Hardin, Jul 17 2016

Status

approved