A061348 Consider a (solid) triangle with n cells on each edge, for a total of n(n+1)/2 cells; a(n) is number of inequivalent ways of labeling cells with 0's and 1's; triangle may be rotated and turned over.

2, 4, 20, 208, 5728, 351616, 44772352, 11453771776, 5864078802944, 6004800040206336, 12297829416834170880, 50371909152808594571264, 412646679762074900658913280, 6760803201217259503457555972096, 221537999297485988040673580072042496

Offset

1,1

Links

Table of n, a(n) for n=1..15.

Formula

See Maple code for formula.

Example

a(2) = 4, the labelings being {000}, {001}, 011}, {111}. Some of the 20 solutions for n=3 are as follows:
..0......1.......0......1.......1.......1.......0
.0.0....0.0.....1.0....1.0.....0.0.....0.0.....1.1
0.0.0..0.0.0...0.0.0..0.0.0...1.0.0...0.1.0...0.0.0
The first solution for n = 4 is
...0
..0.0
.0.0.0
0.0.0.0

Maple

A061348 := proc(n) local t1, v, a; a := n*(n+1)/2; v := floor((n+1)/2); if n mod 3 = 1 then t1 := n*(n+1)/6+2/3; else t1 := n*(n+1)/6; fi; (1/6)*(2^a + 2*2^t1+3*2^(a/2+v/2)); end; # from Burnside's Lemma

Mathematica

A061348[n_] := Module[{t1, v, a}, a = n*(n+1)/2; v = Floor[(n+1)/2]; If[Mod[n, 3] == 1, t1 = n*(n+1)/6+2/3, t1 = n*(n+1)/6]; (1/6)*(2^a+2*2^t1+3*2^(a/2+v/2))]; Table[A061348[n], {n, 1, 15}] (* Jean-François Alcover, Feb 03 2014, after Maple *)

Crossrefs

Cf. A061709.

Sequence in context: A052573 A110371 A120388 * A127103 A059831 A064493

Adjacent sequences: A061345 A061346 A061347 * A061349 A061350 A061351

Keyword

nonn,easy,nice

Author

Michel ten Voorde, Jun 08 2001

Extensions

Formula and more terms from N. J. A. Sloane, Jun 20 2001

Status

approved