A196802 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 3,2,0,4,1 for x=0,1,2,3,4

1, 1, 1, 2, 7, 2, 3, 20, 20, 3, 5, 65, 120, 65, 5, 8, 203, 698, 698, 203, 8, 13, 648, 4078, 7407, 4078, 648, 13, 21, 2057, 23920, 79003, 79003, 23920, 2057, 21, 34, 6527, 140348, 834632, 1516652, 834632, 140348, 6527, 34, 55, 20740, 821284, 8882811, 29239326

Offset

1,4

Comments

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

Table starts

..1.....1........2...........3.............5................8

..1.....7.......20..........65...........203..............648

..2....20......120.........698..........4078............23920

..3....65......698........7407.........79003...........834632

..5...203.....4078.......79003.......1516652.........29239326

..8...648....23920......834632......29239326.......1029024216

.13..2057...140348.....8882811.....567312297......36350586798

.21..6527...821284....94530039...10969537457....1279579729422

.34.20740..4813216..1004745630..212128886217...45097830841266

.55.65833.28205816.10681187595.4104645843820.1589630250146316

Links

R. H. Hardin, Table of n, a(n) for n = 1..161

Example

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

Crossrefs

Column 1 is A000045

Column 2 is A196584

Sequence in context: A197235 A197750 A197098 * A196590 A197047 A273839

Adjacent sequences: A196799 A196800 A196801 * A196803 A196804 A196805

Keyword

nonn,tabl

Author

R. H. Hardin Oct 06 2011

Status

approved