|
Search: id:A061348
|
|
|
| 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 ways of labeling cells with 0's and 1's; triangle may be rotated and turned over. |
|
+0
2
|
|
| 2, 4, 20, 208, 5728, 351616, 44772352, 11453771776, 5864078802944, 6004800040206336, 12297829416834170880, 50371909152808594571264, 412646679762074900658913280, 6760803201217259503457555972096, 221537999297485988040673580072042496
(list; graph; listen)
|
|
|
OFFSET
|
1,1
|
|
|
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, t, v, a; a := n*(n+1)/2; t := floor((n+2)/3); 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
|
|
CROSSREFS
|
Cf. A061709.
Adjacent sequences: A061345 A061346 A061347 this_sequence A061349 A061350 A061351
Sequence in context: A052573 A110371 A120388 this_sequence A127103 A059831 A064493
|
|
KEYWORD
|
nonn,easy,nice
|
|
AUTHOR
|
Michel ten Voorde (seqfan(AT)tenvoorde.org) Jun 08 2001
|
|
EXTENSIONS
|
Formula and more terms from N. J. A. Sloane (njas(AT)research.att.com), Jun 20, 2001
|
|
|
Search completed in 0.002 seconds
|
