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 A054554 a(n) = 4n^2 - 10n + 7. 38
 1, 3, 13, 31, 57, 91, 133, 183, 241, 307, 381, 463, 553, 651, 757, 871, 993, 1123, 1261, 1407, 1561, 1723, 1893, 2071, 2257, 2451, 2653, 2863, 3081, 3307, 3541, 3783, 4033, 4291, 4557, 4831, 5113, 5403, 5701, 6007, 6321, 6643, 6973, 7311, 7657, 8011, 8373 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Move in 1-3 direction in a spiral organized like A068225 etc. Equals binomial transform of [1, 2, 8, 0, 0, 0, ...]. - Gary W. Adamson, May 03 2008 Ulam's spiral (NE spoke). - Robert G. Wilson v, Oct 31 2011 a(k+1) = 4k^2 - 2k + 1 in the Numberphile video. - Frank Ellermann, Mar 11 2020 LINKS Ivan Panchenko, Table of n, a(n) for n = 1..1000 James Grime and Brady Haran, Prime Spirals, Numberphile video (2013). Robert G. Wilson v, Cover of the March 1964 issue of Scientific American Index entries for linear recurrences with constant coefficients, signature (3,-3,1). FORMULA a(n) = 8*n + a(n-1) - 14 with n > 1, a(1)=1. - Vincenzo Librandi, Aug 07 2010 G.f.: -x*(7*x^2+1)/(x-1)^3. - Colin Barker, Sep 21 2012 For n > 2, a(n) = A014105(n) + A014105(n-1). - Bruce J. Nicholson, May 07 2017 MAPLE A054554:=n->4*n^2 -10*n + 7; seq(A054554(k), k=1..100); # Wesley Ivan Hurt, Nov 05 2013 MATHEMATICA f[n_] := 4n^2 -10n + 7; Array[f, 40] (* Vladimir Joseph Stephan Orlovsky, Sep 01 2008 *) PROG (PARI) a(n)=4*n^2-10*n+7 \\ Charles R Greathouse IV, Nov 05 2013 CROSSREFS Cf. A054553, A068225, A054552, A054556, A054567, A054569, A033951. Cf. A014105. Sequences on the four axes of the square spiral: Starting at 0: A001107, A033991, A007742, A033954; starting at 1: A054552, A054556, A054567, A033951. Sequences on the four diagonals of the square spiral: Starting at 0: A002939 = 2*A000384, A016742 = 4*A000290, A002943 = 2*A014105, A033996 = 8*A000217; starting at 1: A054554, A053755, A054569, A016754. Sequences obtained by reading alternate terms on the X and Y axes and the two main diagonals of the square spiral: Starting at 0: A035608, A156859, A002378 = 2*A000217, A137932 = 4*A002620; starting at 1: A317186, A267682, A002061, A080335. Sequence in context: A179026 A179027 A145907 * A051939 A257764 A146728 Adjacent sequences:  A054551 A054552 A054553 * A054555 A054556 A054557 KEYWORD easy,nonn AUTHOR Enoch Haga, G. L. Honaker, Jr., Apr 10 2000 EXTENSIONS Edited by Frank Ellermann, Feb 24 2002 STATUS approved

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Last modified April 20 05:46 EDT 2021. Contains 343121 sequences. (Running on oeis4.)