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A077591
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Maximum number of regions the plane can be divided into using n (concave) quadrilaterals.
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10
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1, 2, 18, 50, 98, 162, 242, 338, 450, 578, 722, 882, 1058, 1250, 1458, 1682, 1922, 2178, 2450, 2738, 3042, 3362, 3698, 4050, 4418, 4802, 5202, 5618, 6050, 6498, 6962, 7442, 7938, 8450, 8978, 9522, 10082, 10658, 11250, 11858, 12482, 13122, 13778
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| For n > 0: A071974(a(n)) = 2*n+1, A071975(a(n)) = 2. [Reinhard Zumkeller, Jul 10 2011]
Sequence found by reading the segment (1, 2) together with the line from 2, in the direction 2, 18,..., in the square spiral whose vertices are the triangular numbers A000217. - Omar E. Pol, Sep 05 2011
For a(n) > 1, a(n) are the numbers such that phi(sum of the odd divisors of a(n)) = phi(sum of even divisors of a(n)). - Michel Lagneau, Sep 14 2011.
Apart from first term, subsequence of A195605. - Bruno Berselli, Sep 21 2011
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 0..10000
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FORMULA
| a(n) = 8*n^2 - 8*n + 2 = 2*(2*n-1)^2, n>0, a(0)=1.
Contribution from Omar E. Pol, Sep 05 2011: (Start)
a(n) = 1 + A069129(n), if n >= 1.
a(n) = 2*A016754(n-1), if n >= 1. (End)
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EXAMPLE
| a(2) = 18 if you draw two concave quadrilaterals such that all four sides of one cross all four sides of the other.
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CROSSREFS
| Cf. A077588.
Sequence in context: A139268 A052681 A048910 * A050808 A058653 A058794
Adjacent sequences: A077588 A077589 A077590 * A077592 A077593 A077594
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KEYWORD
| nonn,easy
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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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