A281205 T(n,k)=Number of nXk 0..1 arrays with no element equal to more than one of its horizontal and antidiagonal neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.

0, 0, 0, 1, 2, 0, 2, 14, 10, 0, 5, 28, 56, 38, 0, 10, 52, 98, 168, 130, 0, 20, 94, 176, 270, 448, 420, 0, 38, 166, 310, 470, 676, 1120, 1308, 0, 71, 290, 537, 804, 1141, 1588, 2688, 3970, 0, 130, 502, 922, 1358, 1906, 2602, 3604, 6272, 11822, 0, 235, 864, 1573, 2284, 3137

Offset: 1

Author

R. H. Hardin, Jan 17 2017

Keywords

• nonn
• tabl

Comments

Table starts

.0.....0.....1.....2.....5....10.....20.....38.....71....130....235.....420

.0.....2....14....28....52....94....166....290....502....864...1480....2526

.0....10....56....98...176...310....537....922...1573...2672...4524....7640

.0....38...168...270...470...804...1358...2284...3834...6432..10786...18080

.0...130...448...676..1141..1906...3137...5160...8510..14084..23379...38894

.0...420..1120..1588..2602..4248...6838..11010..17840..29120..47838...78978

.0..1308..2688..3604..5712..9118..14375..22700..36144..58168..94524..154800

.0..3970..6272..7960.12208.19026..29416..45614..71452.113388.182228..295950

.0.11822.14336.17254.25577.38916..58984..89916.138676.217124.345089..555674

.0.34690.32256.36848.52784.78356.116466.174558.265278.409976.644568.1028978

Examples

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

Links

• R. H. Hardin, Table of n, a(n) for n = 1..421

Crossrefs

Row 1 is A001629(n-1).

Formula

Empirical for column k:

k=1: a(n) = a(n-1)

k=2: a(n) = 6*a(n-1) -11*a(n-2) +6*a(n-3) -a(n-4)

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

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

k=5: a(n) = 4*a(n-1) -4*a(n-2) -2*a(n-4) +4*a(n-5) -a(n-8)

k=6: [order 12]

k=7: [order 12]

Empirical for row n:

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

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

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

n=4: a(n) = 4*a(n-1) -4*a(n-2) -2*a(n-3) +4*a(n-4) -a(n-6) for n>10

n=5: a(n) = 4*a(n-1) -4*a(n-2) -2*a(n-3) +4*a(n-4) -a(n-6) for n>11

n=6: a(n) = 4*a(n-1) -4*a(n-2) -2*a(n-3) +4*a(n-4) -a(n-6) for n>12

n=7: a(n) = 4*a(n-1) -4*a(n-2) -2*a(n-3) +4*a(n-4) -a(n-6) for n>13