A220602 T(n,k)=Number of ways to reciprocally link elements of an nXk array either to themselves or to exactly two horizontal, vertical and antidiagonal neighbors, without 3-loops

1, 1, 1, 1, 2, 1, 1, 7, 7, 1, 1, 17, 65, 17, 1, 1, 44, 471, 471, 44, 1, 1, 117, 3469, 9047, 3469, 117, 1, 1, 305, 25747, 167614, 167614, 25747, 305, 1, 1, 798, 190425, 3174778, 7558495, 3174778, 190425, 798, 1, 1, 2091, 1408823, 60138423, 352586943

Offset

1,5

Comments

Table starts

.1.....1..........1...............1...................1

.1.....2..........7..............17..................44

.1.....7.........65.............471................3469

.1....17........471............9047..............167614

.1....44.......3469..........167614.............7558495

.1...117......25747.........3174778...........352586943

.1...305.....190425........60138423.........16505365334

.1...798....1408823......1137615308........770615995060

.1..2091...10424813.....21523535122......35978245868462

.1..5473...77135267....407249783145....1680090131446571

.1.14328..570740149...7705461280893...78453960278374893

.1.37513.4223043591.145792738613760.3663456651896335065

Links

R. H. Hardin, Table of n, a(n) for n = 1..180

Example

Some solutions for n=3 k=4 0=self 2=n 3=ne 4=w 6=e 7=sw 8=s (reciprocal directions total 10)
.00.68.48.78...00.68.48.00...00.00.67.47...00.67.47.00...00.67.47.00
.68.24.23.28...68.24.28.00...00.38.36.48...36.34.67.47...38.37.68.48
.26.46.46.24...26.46.24.00...00.26.46.24...00.36.34.00...23.00.26.24

Crossrefs

Column 2 is A108479

Sequence in context: A122021 A303817 A158200 * A166345 A015110 A128596

Adjacent sequences: A220599 A220600 A220601 * A220603 A220604 A220605

Keyword

nonn,tabl

Author

R. H. Hardin Dec 16 2012

Status

approved