login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A236283 The number of orbits of triples of {1,2,...,n} under the action of the dihedral group of order 2n. 3
1, 4, 5, 10, 13, 20, 25, 34, 41, 52, 61, 74, 85, 100, 113, 130, 145, 164, 181, 202, 221, 244, 265, 290, 313, 340, 365, 394, 421, 452, 481, 514, 545, 580, 613, 650, 685, 724, 761, 802, 841, 884, 925, 970, 1013, 1060, 1105, 1154, 1201, 1252 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..50.

FORMULA

Conjecture: a(n) = (5+3*(-1)^n+2*n^2)/4. a(n) = 2*a(n-1)-2*a(n-3)+a(n-4). G.f.: -x*(2*x^3-3*x^2+2*x+1) / ((x-1)^3*(x+1)). - Colin Barker, Jan 21 2014

a(n) = A081352(n - 1) - A116940(n - 1). - Miko Labalan, Nov 12 2016

EXAMPLE

For n = 3 there are 5 orbits of triples:

[[1,1,1], [2,2,2], [3,3,3]],

[[1,1,2], [2,2,3], [1,1,3], [3,3,1], [3,3,2], [2,2,1]],

[[1,2,1], [2,3,2], [1,3,1], [3,1,3], [3,2,3], [2,1,2]],

[[1,2,2], [2,3,3], [1,3,3], [3,1,1], [3,2,2], [2,1,1]],

[[1,2,3], [2,3,1], [1,3,2], [3,1,2], [3,2,1], [2,1,3]].

PROG

(GAP)

a:=function(n)

local g, orbs;

g:=DihedralGroup(IsPermGroup, 2*n);

orbs := OrbitsDomain(g, Tuples( [ 1 .. n ], 3), OnTuples );

return Size(orbs);

end;;

CROSSREFS

Sequence in context: A094415 A114517 A283246 * A116930 A073119 A002257

Adjacent sequences:  A236280 A236281 A236282 * A236284 A236285 A236286

KEYWORD

nonn

AUTHOR

W. Edwin Clark, Jan 21 2014

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified November 16 06:50 EST 2018. Contains 317258 sequences. (Running on oeis4.)