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A220614
T(n,k)=Number of ways to reciprocally link elements of an nXk array either to themselves or to exactly two horizontal and vertical neighbors, without consecutive collinear links
4
1, 1, 1, 1, 2, 1, 1, 3, 3, 1, 1, 5, 5, 5, 1, 1, 8, 11, 11, 8, 1, 1, 13, 21, 36, 21, 13, 1, 1, 21, 43, 95, 95, 43, 21, 1, 1, 34, 85, 281, 324, 281, 85, 34, 1, 1, 55, 171, 781, 1277, 1277, 781, 171, 55, 1, 1, 89, 341, 2245, 4673, 7041, 4673, 2245, 341, 89, 1, 1, 144, 683, 6336
OFFSET
1,5
COMMENTS
Table starts
.1...1....1......1.......1.........1..........1............1.............1
.1...2....3......5.......8........13.........21...........34............55
.1...3....5.....11......21........43.........85..........171...........341
.1...5...11.....36......95.......281........781.........2245..........6336
.1...8...21.....95.....324......1277.......4673........17768.........66245
.1..13...43....281....1277......7041......34981.......183920........937663
.1..21...85....781....4673.....34981.....233265......1653229......11354857
.1..34..171...2245...17768....183920....1653229.....16038658.....149429377
.1..55..341...6336...66245....937663...11354857....149429377....1884307184
.1..89..683..18061..249499...4861869...79290645...1423339849...24310532213
.1.144.1365..51205..934816..24977087..548972737..13397669320..309983079825
.1.233.2731.145601.3511945.128971605.3817993565.126938044289.3977585437731
LINKS
EXAMPLE
Some solutions for n=3 k=4 0=self 2=n 4=w 6=e 8=s (reciprocal directions total 10)
.00.00.68.48...68.48.68.48...68.48.00.00...00.00.00.00...00.68.48.00
.00.00.26.24...26.24.26.24...26.24.00.00...00.00.00.00...00.26.24.00
.00.00.00.00...00.00.00.00...00.00.00.00...00.00.00.00...00.00.00.00
CROSSREFS
Column 2 is A000045(n+1)
Column 3 is A001045(n+1)
Column 4 is A005178(n+1)
Diagonal is A086832
Sequence in context: A053538 A235803 A138201 * A154221 A026736 A230859
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin Dec 17 2012
STATUS
approved