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Search: id:A061348
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| A061348 |
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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. |
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+0
2
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| 2, 4, 20, 208, 5728, 351616, 44772352, 11453771776, 5864078802944, 6004800040206336, 12297829416834170880, 50371909152808594571264, 412646679762074900658913280, 6760803201217259503457555972096, 221537999297485988040673580072042496
(list; graph; listen)
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OFFSET
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1,1
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FORMULA
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See Maple code for formula.
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EXAMPLE
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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
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MAPLE
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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
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CROSSREFS
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Cf. A061709.
Sequence in context: A052573 A110371 A120388 this_sequence A127103 A059831 A064493
Adjacent sequences: A061345 A061346 A061347 this_sequence A061349 A061350 A061351
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KEYWORD
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nonn,easy,nice
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AUTHOR
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Michel ten Voorde (seqfan(AT)tenvoorde.org) Jun 08 2001
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EXTENSIONS
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Formula and more terms from N. J. A. Sloane (njas(AT)research.att.com), Jun 20, 2001
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