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 A077591 Maximum number of regions into which the plane can be divided using n (concave) quadrilaterals. 12
 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; text; internal format)
 OFFSET 0,2 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 For n>3, a(n) is the fourth least number k = x + y, with x>0 and y>0, such that there are n different pairs (x,y) for which x*y/k is an integer. - Paolo P. Lava, Jan 29 2018 Engel expansion of 1F2(1;1/2,1/2;1/8). - Benedict W. J. Irwin, Jun 21 2018 LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..10000 FORMULA a(n) = 8*n^2 - 8*n + 2 = 2*(2*n-1)^2, n>0, a(0)=1. [It would be nice to have a proof, or even a reference to a proof. - N. J. A. Sloane, Nov 30 2017] a(n) = 1 + A069129(n), if n >= 1. - Omar E. Pol, Sep 05 2011 a(n) = 2*A016754(n-1), if n >= 1. - Omar E. Pol, Sep 05 2011 G.f.: (1-x+15*x^2+x^3)/(1-x)^3. - Colin Barker, Feb 23 2012 E.g.f.: (8*x^2 + 2)*exp(x) -1. - G. C. Greubel, Jul 15 2017 EXAMPLE a(2) = 18 if you draw two concave quadrilaterals such that all four sides of one cross all four sides of the other. MAPLE A077591:=n->`if`(n=0, 1, 8*n^2 - 8*n + 2); seq(A077591(n), n=0..50); # Wesley Ivan Hurt, Mar 12 2014 MATHEMATICA Table[2*(4*n^2 - 4*n + 1), {n, 0, 50}] (* G. C. Greubel, Jul 15 2017 *) PROG (PARI) isok(n) = (sod = sumdiv(n, d, (d%2)*d)) && (sed = sumdiv(n, d, (1 - d%2)*d)) && (eulerphi(sod) == eulerphi(sed)); \\ from Michel Lagneau comment; Michel Marcus, Mar 15 2014 (GAP) Concatenation(, List([1..2000], n->8*n^2 - 8*n + 2)); # Muniru A Asiru, Jan 29 2018 CROSSREFS Cf. A077588, A239186. Sequence in context: A208652 A223469 A048910 * A050808 A058653 A058794 Adjacent sequences:  A077588 A077589 A077590 * A077592 A077593 A077594 KEYWORD nonn,easy AUTHOR Joshua Zucker and the Castilleja School MathCounts club, Nov 07 2002 STATUS approved

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Last modified October 16 05:51 EDT 2019. Contains 328044 sequences. (Running on oeis4.)