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

Author

R. H. Hardin Dec 18 2012

Keywords

• nonn
• tabl

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

Examples

			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
		

Links

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

Crossrefs

Column 3 is A000045(n+1)

Column 4 is A002478

Row 2 is A000045

Row 3 is A003945(n-2)