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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 9
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 (list; table; graph; refs; listen; history; text; internal format)
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: A335570 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

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Last modified May 18 23:08 EDT 2021. Contains 344008 sequences. (Running on oeis4.)