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.

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

Author

R. H. Hardin Dec 17 2012

Keywords

• nonn
• tabl

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

Examples

			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
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..544

Crossrefs

Column 2 is A000045(n+1)

Column 3 is A001045(n+1)

Column 4 is A005178(n+1)

Diagonal is A086832