A220681 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 consecutive collinear links

1, 1, 1, 1, 4, 1, 1, 9, 9, 1, 1, 25, 43, 25, 1, 1, 64, 201, 201, 64, 1, 1, 169, 968, 2024, 968, 169, 1, 1, 441, 4604, 21380, 21380, 4604, 441, 1, 1, 1156, 22000, 220299, 468036, 220299, 22000, 1156, 1, 1, 3025, 104976, 2316754, 9973284, 9973284, 2316754

Offset

1,5

Comments

Table starts

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

.1.....4........9...........25...............64.................169

.1.....9.......43..........201..............968................4604

.1....25......201.........2024............21380..............220299

.1....64......968........21380...........468036.............9973284

.1...169.....4604.......220299..........9973284...........455249977

.1...441....22000......2316754........215926776.........21051034046

.1..1156...104976.....24198121.......4649097520........969333059888

.1..3025...501096....253601977.....100274426148......44710643494095

.1..7921..2391737...2654925237....2161781726064....2061425679292684

.1.20736.11415981..27806859021...46610315291176...95053260696179636

.1.54289.54489429.291197368229.1004947894341776.4382893797173364311

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)
.00.00.00.00...00.00.00.00...68.48.00.00...00.00.00.78...00.67.47.00
.68.48.68.48...00.68.47.00...26.24.68.48...00.78.36.24...38.38.00.00
.26.24.26.24...00.23.00.00...00.00.26.24...36.24.00.00...26.24.00.00

Crossrefs

Column 2 is A007598(n+1)

Sequence in context: A146767 A146955 A155451 * A189280 A168621 A039756

Adjacent sequences: A220678 A220679 A220680 * A220682 A220683 A220684

Keyword

nonn,tabl

Author

R. H. Hardin Dec 17 2012

Status

approved