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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 7

%I #4 Dec 17 2012 16:02:56

%S 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,

%T 968,169,1,1,441,4604,21380,21380,4604,441,1,1,1156,22000,220299,

%U 468036,220299,22000,1156,1,1,3025,104976,2316754,9973284,9973284,2316754

%N 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

%C Table starts

%C .1.....1........1............1................1...................1

%C .1.....4........9...........25...............64.................169

%C .1.....9.......43..........201..............968................4604

%C .1....25......201.........2024............21380..............220299

%C .1....64......968........21380...........468036.............9973284

%C .1...169.....4604.......220299..........9973284...........455249977

%C .1...441....22000......2316754........215926776.........21051034046

%C .1..1156...104976.....24198121.......4649097520........969333059888

%C .1..3025...501096....253601977.....100274426148......44710643494095

%C .1..7921..2391737...2654925237....2161781726064....2061425679292684

%C .1.20736.11415981..27806859021...46610315291176...95053260696179636

%C .1.54289.54489429.291197368229.1004947894341776.4382893797173364311

%H R. H. Hardin, <a href="/A220681/b220681.txt">Table of n, a(n) for n = 1..180</a>

%e 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)

%e .00.00.00.00...00.00.00.00...68.48.00.00...00.00.00.78...00.67.47.00

%e .68.48.68.48...00.68.47.00...26.24.68.48...00.78.36.24...38.38.00.00

%e .26.24.26.24...00.23.00.00...00.00.26.24...36.24.00.00...26.24.00.00

%Y Column 2 is A007598(n+1)

%K nonn,tabl

%O 1,5

%A _R. H. Hardin_ Dec 17 2012

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Last modified March 28 18:04 EDT 2024. Contains 371254 sequences. (Running on oeis4.)