login
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
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
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: A367074 A177113 A347010 * A285152 A077184 A077183
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Jan 17 2017
STATUS
approved