A276299 T(n,k)=Number of nXk 0..2 arrays with no element equal to any value at offset (-2,-1) (-1,1) or (0,-1) and new values introduced in order 0..2.

1, 1, 2, 2, 4, 5, 4, 12, 11, 14, 8, 36, 45, 31, 41, 16, 108, 173, 189, 88, 122, 32, 324, 693, 1017, 805, 250, 365, 64, 972, 2765, 5909, 5965, 3437, 710, 1094, 128, 2916, 11061, 33461, 50949, 34865, 14693, 2016, 3281, 256, 8748, 44237, 191289, 408105, 442001

Offset

1,3

Comments

Table starts

....1.....1.......2........4..........8...........16............32

....2.....4......12.......36........108..........324...........972

....5....11......45......173........693.........2765.........11061

...14....31.....189.....1017.......5909........33461........191289

...41....88.....805.....5965......50949.......408105.......3363533

..122...250....3437....34865.....442001......4988145......59728757

..365...710...14693...203933....3861469.....61239977....1073114625

.1094..2016...62829..1192701...33851605....752660245...19398127957

.3281..5724..268677..6974781..297360321...9254592049..352134188049

.9842.16252.1148973.40786925.2615328377.113817204341.6411366745009

Links

R. H. Hardin, Table of n, a(n) for n = 1..264

Formula

Empirical for column k:

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

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

k=3: a(n) = 6*a(n-1) -8*a(n-2) +4*a(n-3) -7*a(n-4) +6*a(n-5) for n>7

k=4: [order 11] for n>13

k=5: [order 33] for n>37

k=6: [order 70] for n>75

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

n=4: a(n) = 4*a(n-1) +10*a(n-2) -6*a(n-4) -22*a(n-5) +15*a(n-6) for n>8

n=5: [order 15] for n>17

n=6: [order 30] for n>32

n=7: [order 59] for n>61

Example

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

Crossrefs

Column 1 is A007051(n-1).

Row 1 is A000079(n-2).

Row 2 is A003946(n-1).

Sequence in context: A252938 A229402 A266249 * A231302 A231363 A225840

Adjacent sequences: A276296 A276297 A276298 * A276300 A276301 A276302

Keyword

nonn,tabl

Author

R. H. Hardin, Aug 28 2016

Status

approved