A232309 T(n,k)=Number of nXk 0..2 arrays with every 0 next to a 1 and every 1 next to a 2 horizontally, vertically or antidiagonally

1, 3, 3, 7, 37, 7, 15, 257, 257, 15, 33, 1915, 5149, 1915, 33, 73, 14223, 107047, 107047, 14223, 73, 161, 105411, 2245709, 6363511, 2245709, 105411, 161, 355, 781873, 46996227, 382995685, 382995685, 46996227, 781873, 355, 783, 5798587, 983668985

Offset

1,2

Comments

Table starts

....1.........3.............7.................15......................33

....3........37...........257...............1915...................14223

....7.......257..........5149.............107047.................2245709

...15......1915........107047............6363511...............382995685

...33.....14223.......2245709..........382995685.............66287652717

...73....105411......46996227........22952606015..........11412010021707

..161....781873.....983668985......1376103637041........1965722343353835

..355...5798587...20589521605.....82507009197797......338617181188008457

..783..43004317..430963205159...4946765617435461....58328939899371775421

.1727.318935945.9020580137409.296587635447682217.10047560921392694812519

Links

R. H. Hardin, Table of n, a(n) for n = 1..199

Formula

Empirical for column k:

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

k=2: a(n) = 6*a(n-1) +9*a(n-2) +11*a(n-3) -a(n-4) +16*a(n-5)

k=3: [order 15]

k=4: [order 33]

k=5: [order 91]

Example

Some solutions for n=3 k=4
..2..1..1..1....2..1..1..2....1..2..0..1....2..0..2..2....1..2..2..1
..1..2..0..2....1..2..1..1....1..1..2..1....2..1..2..1....0..1..2..1
..0..2..1..1....1..0..2..0....1..2..1..2....0..0..1..0....1..2..0..2

Crossrefs

Column 1 is A193641

Sequence in context: A191498 A065747 A363398 * A273043 A066142 A232459

Adjacent sequences: A232306 A232307 A232308 * A232310 A232311 A232312

Keyword

nonn,tabl

Author

R. H. Hardin, Nov 22 2013

Status

approved