A196974 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 4,3,0,2,1 for x=0,1,2,3,4

1, 1, 1, 2, 7, 2, 3, 10, 10, 3, 5, 23, 34, 23, 5, 8, 57, 104, 104, 57, 8, 13, 122, 386, 815, 386, 122, 13, 21, 275, 1380, 3675, 3675, 1380, 275, 21, 34, 623, 4800, 20500, 31899, 20500, 4800, 623, 34, 55, 1394, 16794, 115563, 260394, 260394, 115563, 16794, 1394, 55, 89

Offset

1,4

Comments

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

Table starts

..1....1......2........3..........5............8............13..............21

..1....7.....10.......23.........57..........122...........275.............623

..2...10.....34......104........386.........1380..........4800...........16794

..3...23....104......815.......3675........20500........115563..........638791

..5...57....386.....3675......31899.......260394.......2246059........19246379

..8..122...1380....20500.....260394......3602632......47228658.......627332704

.13..275...4800...115563....2246059.....47228658.....986337603.....20278906437

.21..623..16794...638791...19246379....627332704...20278906437....654433849619

.34.1394..58875..3550336..164006734...8353150047..420951074243..21083898963164

.55.3133.206084.19599537.1400773245.111159106170.8734501701701.680696834250493

Links

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

Example

Some solutions for n=6 k=4
..0..2..2..0....0..0..2..0....0..0..0..0....0..2..0..0....0..0..2..0
..0..0..0..0....0..2..2..0....2..2..3..2....2..3..0..2....0..2..3..2
..0..1..0..0....2..3..0..0....0..0..2..0....0..2..0..2....2..3..0..0
..2..3..2..0....0..2..0..0....0..1..3..2....2..3..0..0....0..2..0..0
..0..2..3..2....0..2..3..2....0..0..2..0....0..2..2..2....0..2..2..2
..2..0..0..0....2..0..2..0....2..0..2..0....2..0..0..0....2..0..0..0

Crossrefs

Column 1 is A000045

Column 2 is A196316

Sequence in context: A196322 A197457 A197307 * A197561 A197896 A198013

Adjacent sequences: A196971 A196972 A196973 * A196975 A196976 A196977

Keyword

nonn,tabl

Author

R. H. Hardin Oct 08 2011

Status

approved