A220708 T(n,k)=Number of ways to reciprocally link elements of an nXk array either to themselves or to exactly two horizontal and antidiagonal neighbors, without consecutive collinear links

1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 3, 3, 1, 1, 1, 5, 6, 5, 1, 1, 1, 8, 12, 13, 8, 1, 1, 1, 13, 24, 37, 28, 13, 1, 1, 1, 21, 48, 105, 107, 60, 21, 1, 1, 1, 34, 96, 298, 405, 317, 129, 34, 1, 1, 1, 55, 192, 846, 1520, 1617, 932, 277, 55, 1, 1, 1, 89, 384, 2404, 5706, 8338, 6412, 2749, 595

Offset

1,8

Comments

Table starts

.1.1...1....1......1.......1.........1..........1............1.............1

.1.1...2....3......5.......8........13.........21...........34............55

.1.1...3....6.....12......24........48.........96..........192...........384

.1.1...5...13.....37.....105.......298........846.........2404..........6826

.1.1...8...28....107.....405......1520.......5706........21418.........80390

.1.1..13...60....317....1617......8338......42873.......221082.......1139020

.1.1..21..129....932....6412.....44976.....311193......2168111......15034974

.1.1..34..277...2749...25449....244029....2282408.....21692285.....204339688

.1.1..55..595...8101..101029...1322551...16699080....216083336....2751764573

.1.1..89.1278..23881..400986...7171769..122254180...2156218093...37166744488

.1.1.144.2745..70392.1591697..38885648..894932114..21512078437..501632637139

.1.1.233.5896.207497.6317904.210854845.6551231662.214655813486.6771890123950

Links

R. H. Hardin, Table of n, a(n) for n = 1..391

Example

Some solutions for n=3 k=4 0=self 3=ne 4=w 6=e 7=sw (reciprocal directions total 10)
.00.67.47.00...00.00.00.00...00.00.67.47...00.00.00.00...00.67.47.00
.36.34.00.00...00.00.00.00...00.36.34.00...00.00.67.47...36.34.67.47
.00.00.00.00...00.00.00.00...00.00.00.00...00.36.34.00...00.36.34.00

Crossrefs

Column 3 is A000045(n+1)

Column 4 is A002478

Row 2 is A000045

Row 3 is A003945(n-2)

Sequence in context: A362644 A323718 A130580 * A110541 A331461 A238016

Adjacent sequences: A220705 A220706 A220707 * A220709 A220710 A220711

Keyword

nonn,tabl

Author

R. H. Hardin Dec 18 2012

Status

approved