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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. 14
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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,5

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

LINKS

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

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

EXAMPLE

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

CROSSREFS

Row 1 is A001629(n-1).

Sequence in context: A122496 A230813 A177113 * A285152 A077184 A077183

Adjacent sequences:  A281202 A281203 A281204 * A281206 A281207 A281208

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Jan 17 2017

STATUS

approved

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Last modified January 23 10:36 EST 2020. Contains 331171 sequences. (Running on oeis4.)