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 A137928 The even principal diagonal of a 2n X 2n square spiral. 14
 2, 4, 10, 16, 26, 36, 50, 64, 82, 100, 122, 144, 170, 196, 226, 256, 290, 324, 362, 400, 442, 484, 530, 576, 626, 676, 730, 784, 842, 900, 962, 1024, 1090, 1156, 1226, 1296, 1370, 1444, 1522, 1600, 1682, 1764, 1850, 1936, 2026, 2116, 2210, 2304, 2402, 2500, 2602, 2704, 2810 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS This is concerned with 2n X 2n square spirals of the form illustrated in the Example section. LINKS Index entries for linear recurrences with constant coefficients, signature (2,0,-2,1) FORMULA a(n) = 2*n + 4*floor((n-1)^2/4) = 2*n + 4*A002620(n-1). a(n) = A171218(n) - A171218(n-1). - Reinhard Zumkeller, Dec 05 2009 From R. J. Mathar, Jun 27 2011: (Start) G.f.: 2*x*(1 + x^2) / ( (1 + x)*(1 - x)^3 ). a(n) = 2*A000982(n). (End) a(n+1) = (3 + 4*n + 2*n^2 + (-1)^n)/2 = A080335(n) + (-1)^n. - Philippe Deléham, Feb 17 2012 a(n) = 2 * ceiling(n^2/2). - Wesley Ivan Hurt, Jun 15 2013 a(n) = n^2 + (n mod 2). - Bruno Berselli, Oct 03 2017 EXAMPLE Example with n = 2: .    7---8---9--10    |           |    6   1---2  11    |       |   |    5---4---3  12                |   16--15--14--13 . a(1) = 2(1) + 4*floor((1-1)/4) = 2; a(2) = 2(2) + 4*floor((2-1)/4) = 4. MAPLE A137928:=n->2*ceil(n^2/2): seq(A137928(n), n=1..100); # Wesley Ivan Hurt, Jul 25 2017 MATHEMATICA LinearRecurrence[{2, 0, -2, 1}, {2, 4, 10, 16}, 60] (* Harvey P. Dale, Aug 28 2017 *) PROG (Python) a = lambda n: 2*n + 4*floor((n-1)**2/4) (PARI) a(n)=2*n+(n-1)^2\4*4 \\ Charles R Greathouse IV, May 21 2015 CROSSREFS Cf. A000982, A002061 (odd diagonal), A002620, A080335, A171218. Sequence in context: A189558 A111149 A123689 * A293154 A144834 A006584 Adjacent sequences:  A137925 A137926 A137927 * A137929 A137930 A137931 KEYWORD nonn,easy AUTHOR William A. Tedeschi, Feb 29 2008 STATUS approved

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Last modified October 17 19:36 EDT 2018. Contains 316293 sequences. (Running on oeis4.)