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

Author

R. H. Hardin, Aug 28 2016

Keywords

• nonn
• tabl

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

Examples

			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
		

Links

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

Crossrefs

Column 1 is A007051(n-1).

Row 1 is A000079(n-2).

Row 2 is A003946(n-1).

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