The OEIS is supported by the many generous donors to the OEIS Foundation.

 Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 59th year, we have over 358,000 sequences, and we’ve crossed 10,300 citations (which often say “discovered thanks to the OEIS”). Other ways to Give
 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A014634 a(n) = (2*n+1)*(4*n+1). 24
 1, 15, 45, 91, 153, 231, 325, 435, 561, 703, 861, 1035, 1225, 1431, 1653, 1891, 2145, 2415, 2701, 3003, 3321, 3655, 4005, 4371, 4753, 5151, 5565, 5995, 6441, 6903, 7381, 7875, 8385, 8911, 9453, 10011, 10585, 11175, 11781, 12403, 13041, 13695, 14365, 15051 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Odd hexagonal numbers. Bisection of A000384. - Omar E. Pol, Apr 06 2008 Sequence found by reading the line from 1, in the direction 1, 15, ..., in the square spiral whose vertices are the triangular numbers A000217. - Omar E. Pol, Sep 03 2011 a(n) is also the sum of natural numbers which can be placed in a center box and expanded ones on 4 arms on N, S, E, W or NE, NW, SW, SE directions. See illustration in links. - Kival Ngaokrajang, Jul 08 2014 LINKS G. C. Greubel, Table of n, a(n) for n = 0..5000 Kival Ngaokrajang, Illustration of initial terms. Leo Tavares, Illustration: Dual Square Stars Index entries for linear recurrences with constant coefficients, signature (3,-3,1). FORMULA a(n) = A157870(n)/2. - Vladimir Joseph Stephan Orlovsky, Mar 10 2009 a(n) = a(n-1) + 16*n-2 (with a(0)=1). - Vincenzo Librandi, Nov 20 2010 G.f.: (1+12*x+3*x^2)/(1-x)^3. - Colin Barker, Jan 08 2012 a(n) = A005408(n) * A016813(n). - Omar E. Pol, Nov 05 2013 a(n) = 2*A033954(n) + 1 = A194268(n) - n. - Wesley Ivan Hurt, Jul 14 2014 E.g.f.: (8*x^2 +14*x + 1)*exp(x). - G. C. Greubel, Jul 18 2017 From Amiram Eldar, Feb 28 2022: (Start) Sum_{n>=0} 1/a(n) = Pi/4 + log(2)/2. Sum_{n>=0} (-1)^n/a(n) = Pi*(sqrt(2)-1)/4 + log(sqrt(2)+1)/sqrt(2). (End) a(n) = A003154(n+1) + 2*A000290(n). - Leo Tavares, Mar 26 2022 MAPLE A014634:=n->(2*n+1)*(4*n+1); seq(A014634(k), k=0..100); # Wesley Ivan Hurt, Nov 04 2013 MATHEMATICA lst={}; Do[a=(2*n+1)*(4*n+1); AppendTo[lst, a], {n, 0, 5!}]; lst (* Vladimir Joseph Stephan Orlovsky, Mar 10 2009 *) Table[(2 n + 1) (4 n + 1), {n, 0, 50}] (* Wesley Ivan Hurt, Jul 09 2014 *) LinearRecurrence[{3, -3, 1}, {1, 15, 45}, 50] (* Harvey P. Dale, Aug 30 2021 *) PROG (Magma) [(2*n+1)*(4*n+1) : n in [0..50]]; // Wesley Ivan Hurt, Jul 09 2014 (PARI) a(n)=(2*n+1)*(4*n+1) \\ Charles R Greathouse IV, Sep 24 2015 CROSSREFS Cf. A000217, A000384, A005408, A016813, A033954, A157870, A194268. Cf. A003154, A000290. Sequence in context: A033849 A194715 A060536 * A303857 A278337 A270563 Adjacent sequences: A014631 A014632 A014633 * A014635 A014636 A014637 KEYWORD nonn,easy AUTHOR EXTENSIONS More terms from Wesley Ivan Hurt, Jul 09 2014 STATUS approved

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

Last modified December 5 15:27 EST 2022. Contains 358588 sequences. (Running on oeis4.)