A204607 T(n,k)=Number of (n+2)X(k+2) 0..2 arrays with every 3X3 subblock having three strictly increasing elements in a row horizontally, vertically or nw-to-se diagonally exactly one way

3562, 29678, 29678, 328845, 144168, 328845, 2275645, 741296, 741296, 2275645, 16247580, 4820300, 981914, 4820300, 16247580, 153711850, 40672735, 5260434, 5260434, 40672735, 153711850, 1240455298, 304865717, 43980907, 10978524

Offset

1,1

Comments

Table starts

.......3562.......29678......328845.....2275645....16247580...153711850

......29678......144168......741296.....4820300....40672735...304865717

.....328845......741296......981914.....5260434....43980907...327968423

....2275645.....4820300.....5260434....10978524....69792825...774393122

...16247580....40672735....43980907....69792825...207096000..1139760144

..153711850...304865717...327968423...774393122..1139760144..1719348416

.1240455298..1982068849..2572437376..4518555426..6656676736..9620299328

.9111381604.16593833004.19830769591.32448416953.61015724528.81184579243

Links

R. H. Hardin, Table of n, a(n) for n = 1..611

Formula

Empirical for column k:

k=1: (order 24 recurrence)

k=2: (order 30 recurrence for n>33)

k=3: a(n) = 442*a(n-3) +63*a(n-5) +43*a(n-6) -63*a(n-8) +81*a(n-9) -81*a(n-12) for n>20

k=4: a(n) = 442*a(n-3) +43*a(n-6) for n>15

k=5: a(n) = 442*a(n-3) +43*a(n-6) for n>16

k=6: a(n) = 442*a(n-3) +43*a(n-6) for n>17

k=7: a(n) = 442*a(n-3) +43*a(n-6) for n>18

Example

Some solutions for n=3 k=3
..0..2..0..0..0....2..1..1..0..2....2..0..0..0..2....2..0..1..1..2
..2..2..0..1..0....1..2..2..1..0....1..1..1..0..2....0..1..0..1..2
..0..1..2..2..1....0..1..2..2..1....1..0..2..1..0....1..2..1..1..0
..1..0..1..2..2....1..0..1..2..2....0..1..2..2..1....2..0..1..2..1
..0..0..0..1..2....1..0..0..1..2....1..0..1..2..2....0..1..2..0..2

Crossrefs

Sequence in context: A083955 A104207 A107646 * A204600 A204599 A206090

Adjacent sequences: A204604 A204605 A204606 * A204608 A204609 A204610

Keyword

nonn,tabl

Author

R. H. Hardin Jan 17 2012

Status

approved