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A077588
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Maximum number of regions the plane is divided into by n triangles.
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3
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1, 2, 8, 20, 38, 62, 92, 128, 170, 218, 272, 332, 398, 470, 548, 632, 722, 818, 920, 1028, 1142, 1262, 1388, 1520, 1658, 1802, 1952, 2108, 2270, 2438, 2612, 2792, 2978, 3170, 3368, 3572, 3782, 3998, 4220, 4448, 4682, 4922, 5168, 5420, 5678, 5942, 6212, 6488
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| a(n) = A096777(3*n-1) for n>0. - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Dec 29 2007
a(n) = a(n-1) + 6*n - 6 (with a(1) = 2) [From Vincenzo Librandi, Dec 07 2010]
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FORMULA
| a(n) = 3n^2 - 3n + 2 except when n = 0.
Nearest integer to sum(k>=n, 1/k^2)/sum(k>=n, 1/k^4) - Benoit Cloitre (benoit7848c(AT)orange.fr), Jun 12 2003
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EXAMPLE
| a(2) = 8 because a Jewish star has 6 points, an interior hexagon and the exterior.
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MATHEMATICA
| CoefficientList[Series[(-z^3 - 5*z^2 + z - 1)/(z - 1)^3, {z, 0, 100}], z] (* From Vladimir Joseph Stephan Orlovsky, Jul 11 2011 *)
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CROSSREFS
| Cf. A077591.
Sequence in context: A031114 A130238 A038460 * A025219 A032767 A032633
Adjacent sequences: A077585 A077586 A077587 * A077589 A077590 A077591
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KEYWORD
| easy,nonn
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AUTHOR
| Joshua Zucker and the Castilleja School mathcounts club (joshua.zucker(AT)stanfordalumni.org), Nov 07 2002
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