A220595 T(n,k) = Number of ways to reciprocally link elements of an n X k array either to themselves or to exactly two king-move neighbors.

1, 1, 1, 1, 8, 1, 1, 33, 33, 1, 1, 155, 423, 155, 1, 1, 710, 6156, 6156, 710, 1, 1, 3265, 87542, 308246, 87542, 3265, 1, 1, 15009, 1250507, 14637699, 14637699, 1250507, 15009, 1, 1, 68992, 17847210, 702811381, 2255735554, 702811381, 17847210, 68992

Offset

1,5

Comments

Table starts

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

.1.......8..........33............155..............710..............3265

.1......33.........423...........6156............87542...........1250507

.1.....155........6156.........308246.........14637699.........702811381

.1.....710.......87542.......14637699.......2255735554......353961472626

.1....3265.....1250507......702811381.....353961472626...182840438017294

.1...15009....17847210....33667621356...55328483420671.93925801702787503

.1...68992...254759570..1613595307718.8656054653129245

.1..317149..3636434730.77327320807492

.1.1457879.51906768670

.1.6701646

.1

Links

R. H. Hardin, Table of n, a(n) for n = 1..84

Example

Some solutions for n=3 k=4 0=self 1=nw 2=n 3=ne 4=w 6=e 7=sw 8=s 9=se (reciprocal directions total 10).
.89.79.69.48...00.68.48.00...00.79.67.47...68.47.78.00...00.00.69.48
.23.16.14.12...00.28.26.47...39.37.13.00...23.38.28.00...89.79.78.12
.00.00.00.00...00.26.34.00...36.14.00.00...00.26.24.00...23.13.12.00

Crossrefs

Sequence in context: A141686 A185412 A157148 * A154335 A142467 A142175

Adjacent sequences: A220592 A220593 A220594 * A220596 A220597 A220598

Keyword

nonn,tabl

Author

R. H. Hardin, Dec 16 2012

Status

approved