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A061709
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Consider a (hollow) triangle with n cells on each edge, for a total of 3(n-1) cells if n>1, or 1 cell if n=1; 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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1
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1, 4, 20, 104, 752, 5600, 44224, 350592, 2800384, 22377984, 178990080, 1431721984, 11453509632, 91626496000, 733009854464, 5864066220032, 46912512917504, 375300002545664, 3002399885885440, 24019198281252864, 192153585175232512
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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FORMULA
| (1/6)*(2^(3*(n-1))+2^n+3*2^(floor((3*n-1)/2))) for n>1.
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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
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CROSSREFS
| Cf. A061348.
Sequence in context: A026305 A195256 A131786 * A135159 A190724 A020084
Adjacent sequences: A061706 A061707 A061708 * A061710 A061711 A061712
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KEYWORD
| nonn,easy,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Jun 20, 2001
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