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A077588 Maximum number of regions the plane is divided into by n triangles. 5
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; text; internal format)
OFFSET

0,2

COMMENTS

a(n) = A096777(3*n-1) for n>0. - Reinhard Zumkeller, Dec 29 2007

a(n) = a(n-1) + 6*n - 6 (with a(1) = 2). - Vincenzo Librandi, Dec 07 2010

For n>0, a(n) = 2 * A005448(n). - Jon Perry, Apr 14 2013

LINKS

Table of n, a(n) for n=0..47.

Luis Manuel Rivera, Integer sequences and k-commuting permutations, arXiv preprint arXiv:1406.3081, 2014

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, Jun 12 2003

For n>0, a(n) = (n-2)*(n-1) + (n-1)*n + n*(n+1). - Jon Perry, Apr 14 2013

EXAMPLE

a(2) = 8 because a Star of David has 6 points, an interior hexagon and the exterior.

MATHEMATICA

CoefficientList[Series[(-z^3 - 5*z^2 + z - 1)/(z - 1)^3, {z, 0, 100}], z] (* Vladimir Joseph Stephan Orlovsky, Jul 11 2011 *)

CROSSREFS

Cf. A077591.

Cf. A005448.

Sequence in context: A130238 A038460 A278212 * A025219 A032767 A032633

Adjacent sequences:  A077585 A077586 A077587 * A077589 A077590 A077591

KEYWORD

easy,nonn

AUTHOR

Joshua Zucker and the Castilleja School mathcounts club, Nov 07 2002

STATUS

approved

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Last modified April 28 16:04 EDT 2017. Contains 285578 sequences.