A196929 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 1,4,3,2,0 for x=0,1,2,3,4

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 3, 3, 1, 1, 1, 1, 5, 7, 5, 1, 1, 1, 1, 8, 17, 17, 8, 1, 1, 1, 1, 13, 41, 65, 41, 13, 1, 1, 1, 1, 21, 99, 231, 231, 99, 21, 1, 1, 1, 1, 34, 239, 833, 1242, 833, 239, 34, 1, 1, 1, 1, 55, 577, 3023, 6755, 6755, 3023, 577, 55, 1, 1, 1, 1, 89

Offset

1,13

Comments

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

Table starts

.1.1..1....1.....1.......1........1.........1...........1............1

.1.1..1....1.....1.......1........1.........1...........1............1

.1.1..2....3.....5.......8.......13........21..........34...........55

.1.1..3....7....17......41.......99.......239.........577.........1393

.1.1..5...17....65.....231......833......3023.......10988........39907

.1.1..8...41...231....1242.....6755.....36867......201212......1098095

.1.1.13...99...833....6755....55546....454787.....3731468.....30604579

.1.1.21..239..3023...36867...454787...5603265....69095695....851871759

.1.1.34..577.10988..201212..3731468..69095695..1280956817..23735291770

.1.1.55.1393.39907.1098095.30604579.851871759.23735291770.661075536443

Links

R. H. Hardin, Table of n, a(n) for n = 1..312

Example

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

Crossrefs

Column 3 is A000045

Column 4 is A001333(n-1)

Sequence in context: A245013 A219924 A226444 * A322494 A258445 A129179

Adjacent sequences: A196926 A196927 A196928 * A196930 A196931 A196932

Keyword

nonn,tabl

Author

R. H. Hardin Oct 07 2011

Status

approved