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A061776
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Start with a single triangle; at n-th generation add a triangle at each vertex, allowing triangles to overlap; sequence gives number of triangles in n-th generation.
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3
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1, 3, 6, 12, 18, 30, 42, 66, 90, 138, 186, 282, 378, 570, 762, 1146, 1530, 2298, 3066, 4602, 6138, 9210, 12282, 18426, 24570, 36858, 49146, 73722, 98298, 147450, 196602, 294906, 393210, 589818, 786426, 1179642, 1572858, 2359290
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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REFERENCES
| R. Reed, The Lemming Simulation Problem, Math. in School, 3 (#6, Nov. 1974), 5-6.
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FORMULA
| Explicit formula given in Maple line.
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MAPLE
| A061776 := proc(n) if n mod 2 = 0 then 6*(2^(n/2)-1); else 3*(2^((n-1)/2)-1)+3*(2^((n+1)/2)-1); fi; end; # for n >= 1
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MATHEMATICA
| a[0]=1; a[n_/; EvenQ[n]]:=6*(2^(n/2)-1); a[n_/; OddQ[n]] := 3*(2^((n-1)/2)-1) + 3*(2^((n+1)/2)-1); a /@ Range[0, 37] (* From Jean-François Alcover, Apr 22 2011, after Maple program *)
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CROSSREFS
| A061777 gives total population of triangles at n-th generation.
Sequence in context: A116958 A006156 A171370 * A074899 A180622 A125851
Adjacent sequences: A061773 A061774 A061775 * A061777 A061778 A061779
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KEYWORD
| nonn,nice,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), R. K. Guy, Jun 23 2001
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