A197047 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 4,2,0,1,3 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, 4080, 7407, 4080, 648, 13, 21, 2057, 24074, 79785, 79785, 24074, 2057, 21, 34, 6527, 141856, 855746, 1563352, 855746, 141856, 6527, 34, 55, 20740, 833758, 9248339, 31096170

Offset

1,4

Comments

Every 0 is next to 0 4'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 3's

Table starts

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

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

..2....20......120.........698..........4080............24074

..3....65......698........7407.........79785...........855746

..5...203.....4080.......79785.......1563352.........31096170

..8...648....24074......855746......31096170.......1146653592

.13..2057...141856.....9248339.....621506173......42346212260

.21..6527...833758....99900759...12367566377....1557004531014

.34.20740..4909544..1077578216..246209727883...57353100417462

.55.65833.28899922.11625151797.4904183446578.2112382332611192

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..0....0..0..0..0....0..0..0..0....0..0..0..0
..0..1..0..2....0..0..0..1....0..0..0..0....0..2..2..2....0..0..1..2
..1..2..0..1....0..0..0..2....0..0..0..0....0..2..0..0....2..0..1..0
..0..0..0..0....2..2..1..0....0..0..2..1....0..1..1..0....2..0..2..2
..2..1..0..0....0..0..1..2....0..2..2..0....0..1..2..0....0..0..0..0
..0..0..2..1....2..0..0..0....0..2..0..2....0..0..0..2....2..0..0..2

Crossrefs

Column 1 is A000045

Column 2 is A196584

Sequence in context: A197098 A196802 A196590 * A273839 A074473 A021371

Adjacent sequences: A197044 A197045 A197046 * A197048 A197049 A197050

Keyword

nonn,tabl

Author

R. H. Hardin Oct 08 2011

Status

approved