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

1,5

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

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

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

Adjacent sequences: A220611 A220612 A220613 * A220615 A220616 A220617

Keyword

nonn,tabl

Author

R. H. Hardin Dec 17 2012

Status

approved