A196590 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 3,2,0,1,4 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, 24032, 79091, 79091, 24032, 2057, 21, 34, 6527, 141460, 839370, 1522940, 839370, 141460, 6527, 34, 55, 20740, 830652, 8980645, 29573040

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 1's, every 4 is next to 4 4's

Table starts

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

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

..2....20......120.........698..........4078............24032

..3....65......698........7407.........79091...........839370

..5...203.....4078.......79091.......1522940.........29573040

..8...648....24032......839370......29573040.......1051645368

.13..2057...141460.....8980645.....578185580......37529013812

.21..6527...830652....96049685...11258527547....1334022464052

.34.20740..4886324..1025896374..219297645143...47492318713306

.55.65833.28734972.10959530915.4274120207800.1690727011393186

Links

R. H. Hardin, Table of n, a(n) for n = 1..144

Example

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

Crossrefs

Column 1 is A000045

Sequence in context: A197750 A197098 A196802 * A197047 A273839 A074473

Adjacent sequences: A196587 A196588 A196589 * A196591 A196592 A196593

Keyword

nonn,tabl

Author

R. H. Hardin Oct 04 2011

Status

approved