A196912 T(n,k)=Number of nXk 0..4 arrays with each element x equal to the number of its horizontal and vertical neighbors equal to 3,1,2,0,4 for x=0,1,2,3,4

1, 2, 2, 3, 6, 3, 4, 13, 13, 4, 6, 34, 50, 34, 6, 9, 81, 193, 193, 81, 9, 13, 199, 731, 1193, 731, 199, 13, 19, 487, 2843, 7290, 7290, 2843, 487, 19, 28, 1190, 10970, 45491, 72523, 45491, 10970, 1190, 28, 41, 2910, 42213, 280860, 733802, 733802, 280860, 42213

Offset

1,2

Comments

Every 0 is next to 0 3's, every 1 is next to 1 1's, every 2 is next to 2 2's, every 3 is next to 3 0's, every 4 is next to 4 4's

Table starts

..1....2......3........4..........6............9..............13

..2....6.....13.......34.........81..........199.............487

..3...13.....50......193........731.........2843...........10970

..4...34....193.....1193.......7290........45491..........280860

..6...81....731.....7290......72523.......733802.........7352954

..9..199...2843....45491.....733802.....12186565.......200038888

.13..487..10970...280860....7352954....200038888......5388703976

.19.1190..42213..1735427...73779592...3288093050....145478400315

.28.2910.162766.10739750..741354396..54146489903...3933296800409

.41.7115.627709.66445820.7448048514.891524201851.106294282176389

Links

R. H. Hardin, Table of n, a(n) for n = 1..180

Example

Some solutions for n=6 k=4
..1..1..0..0....1..0..0..0....0..0..0..0....2..2..2..2....0..0..1..0
..0..0..1..1....1..0..0..0....1..0..0..0....2..0..0..2....0..0..1..0
..1..1..0..0....0..0..2..2....1..0..1..1....2..1..0..2....0..0..0..0
..2..2..0..0....1..1..2..2....0..0..2..2....2..1..2..2....0..1..2..2
..2..2..1..1....2..2..1..0....1..1..2..2....2..2..2..1....0..1..2..2
..1..1..0..0....2..2..1..0....0..0..0..0....1..1..0..1....0..0..0..0

Crossrefs

Column 1 is A000930(n+1)

Sequence in context: A294034 A210220 A075196 * A197079 A208340 A308503

Adjacent sequences: A196909 A196910 A196911 * A196913 A196914 A196915

Keyword

nonn,tabl

Author

R. H. Hardin Oct 07 2011

Status

approved