This site is supported by donations to The OEIS Foundation. Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A054569 a(n) = 4*n^2 - 6*n + 3. 45
 1, 7, 21, 43, 73, 111, 157, 211, 273, 343, 421, 507, 601, 703, 813, 931, 1057, 1191, 1333, 1483, 1641, 1807, 1981, 2163, 2353, 2551, 2757, 2971, 3193, 3423, 3661, 3907, 4161, 4423, 4693, 4971, 5257, 5551, 5853, 6163, 6481, 6807, 7141, 7483, 7833, 8191 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Move in 1-7 direction in a spiral organized like A068225 etc. Third row of A082039. - Paul Barry, Apr 02 2003 Inverse binomial transform of A036826. - Paul Barry, Jun 11 2003 Equals the "middle sequence" T(2*n,n) of the Connell sequence A001614 as a triangle. - Johannes W. Meijer, May 20 2011 Ulam's spiral (SW spoke). - Robert G. Wilson v, Oct 31 2011 LINKS Harvey P. Dale, Table of n, a(n) for n = 1..1000 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+1) = 4*n^2+2*n+1. - Paul Barry, Apr 02 2003 a(n) = 4*n^2-6*n+3-3*0^n (with leading zero). - Paul Barry, Jun 11 2003 Binomial transform of [1, 6, 8, 0, 0, 0,...]. - Gary W. Adamson, Dec 28 2007 a(n) = 8*n+a(n-1)-10 (with a(1)=1). - Vincenzo Librandi, Aug 07 2010 From Colin Barker, Mar 23 2012: (Start) a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). G.f.: x*(1+x)*(1+3*x)/(1-x)^3. (End) a(n) = A000384(n) + A000384(n-1). - Bruce J. Nicholson, May 07 2017 E.g.f.: -3 + (3 - 2*x + 4*x^2)*exp(x). - G. C. Greubel, Jul 04 2019 MATHEMATICA f[n_]:= 4*n^2-6*n+3; Array[f, 50] (* Vladimir Joseph Stephan Orlovsky, Sep 02 2008 *) LinearRecurrence[{3, -3, 1}, {1, 7, 21}, 50] (* Harvey P. Dale, Nov 17 2012 *) PROG (PARI) a(n)=4*n^2-6*n+3 \\ Charles R Greathouse IV, Sep 24 2015 (MAGMA) [4*n^2-6*n+3: n in [1..50]]; // G. C. Greubel, Jul 04 2019 (Sage) [4*n^2-6*n+3 for n in (1..50)] # G. C. Greubel, Jul 04 2019 (GAP) List([1..50], n-> 4*n^2-6*n+3) # G. C. Greubel, Jul 04 2019 CROSSREFS Cf. A000384, A033951, A054552, A054554, A054556, A054567, A054568, A068225. 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: A024966 A226252 A022602 * A077354 A246430 A256051 Adjacent sequences:  A054566 A054567 A054568 * A054570 A054571 A054572 KEYWORD easy,nonn AUTHOR Enoch Haga, G. L. Honaker, Jr., Apr 10 2000 EXTENSIONS Edited by Frank Ellermann, Feb 24 2002 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified October 21 14:06 EDT 2019. Contains 328300 sequences. (Running on oeis4.)