A220553 T(n,k)=Number of ways to reciprocally link elements of an nXk array either to themselves or to exactly one horizontal, vertical or antidiagonal neighbor

1, 2, 2, 3, 8, 3, 5, 29, 29, 5, 8, 108, 224, 108, 8, 13, 401, 1814, 1814, 401, 13, 21, 1490, 14556, 32173, 14556, 1490, 21, 34, 5536, 117022, 565061, 565061, 117022, 5536, 34, 55, 20569, 940432, 9943416, 21668208, 9943416, 940432, 20569, 55, 89, 76424

Offset

1,2

Comments

Table starts

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

...2.......8..........29.............108.................401

...3......29.........224............1814...............14556

...5.....108........1814...........32173..............565061

...8.....401.......14556..........565061............21668208

..13....1490......117022.........9943416...........832899775

..21....5536......940432.......174911750.........32001129185

..34...20569.....7558245......3077034244.......1229633337183

..55...76424....60744605.....54130248568......47247493674864

..89..283953...488197825....952245176313....1815445803499208

.144.1055026..3923590632..16751640356635...69756959373004005

.233.3919944.31533457665.294690365449276.2680352078247056300

Links

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

Example

Some solutions for n=3 k=4 0=self 2=n 3=ne 4=w 6=e 7=sw 8=s (reciprocal directions total 10)
..8..8..0..7....0..6..4..0....0..0..6..4....6..4..7..0....0..0..0..0
..2..2..3..0....0..7..0..7....0..0..6..4....0..3..8..0....8..0..0..8
..0..0..6..4....3..0..3..0....0..0..6..4....0..0..2..0....2..6..4..2

Crossrefs

Column 1 is A000045(n+1)

Sequence in context: A267644 A204197 A238654 * A176383 A100551 A267667

Adjacent sequences: A220550 A220551 A220552 * A220554 A220555 A220556

Keyword

nonn,tabl

Author

R. H. Hardin Dec 15 2012

Status

approved