This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A139272 a(n) = n*(8*n-5). 12
 0, 3, 22, 57, 108, 175, 258, 357, 472, 603, 750, 913, 1092, 1287, 1498, 1725, 1968, 2227, 2502, 2793, 3100, 3423, 3762, 4117, 4488, 4875, 5278, 5697, 6132, 6583, 7050, 7533, 8032, 8547, 9078, 9625, 10188, 10767, 11362, 11973, 12600 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Sequence found by reading the line from 0, in the direction 0, 3, ..., in the square spiral whose vertices are the triangular numbers A000217. Opposite numbers to the members of A139276 in the same spiral. LINKS G. C. Greubel, Table of n, a(n) for n = 0..5000 Franck Ramaharo, Statistics on some classes of knot shadows, arXiv:1802.07701 [math.CO], 2018. Index entries for linear recurrences with constant coefficients, signature (3,-3,1). FORMULA a(n) = 8*n^2 - 5*n. Sequences of the form a(n) = 8*n^2 + c*n have generating functions x{c+8+(8-c)x} / (1-x)^3 and recurrence a(n) = 3a(n-1) - 3a(n-2) + a(n-3). The inverse binomial transform is 0, c+8, 16, 0, 0, ... (0 continued). This applies to A139271-A139278, positive or negative c. - R. J. Mathar, May 12 2008 a(n) = 16*n + a(n-1) - 13 with n>0, a(0)=0. - Vincenzo Librandi, Aug 03 2010 From G. C. Greubel, Jul 18 2017: (Start) a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). G.f.: x*(13*x + 3)/(1-x)^3. E.g.f.: (8*x^2 + 3*x)*exp(x). (End) MATHEMATICA s=0; lst={s}; Do[s+=n++ +3; AppendTo[lst, s], {n, 0, 7!, 16}]; lst (* Vladimir Joseph Stephan Orlovsky, Nov 16 2008 *) Table[n*(8*n -5), {n, 0, 50}] (* G. C. Greubel, Jul 18 2017 *) PROG (PARI) a(n)=n*(8*n-5) \\ Charles R Greathouse IV, Oct 07 2015 CROSSREFS Cf. A000217, A014634, A014635, A033585, A033586, A033587, A035008, A051870, A069129, A085250, A072279, A139273, A139274, A139275, A139276, A139278, A139279, A139280, A139281, A139282. Cf. numbers of the form n*(n*k-k+6))/2, this sequence is the case k=16: see Comments lines of A226492. Sequence in context: A225414 A187694 A104604 * A159345 A006532 A274870 Adjacent sequences:  A139269 A139270 A139271 * A139273 A139274 A139275 KEYWORD nonn,easy AUTHOR Omar E. Pol, Apr 26 2008 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 August 22 20:43 EDT 2019. Contains 326198 sequences. (Running on oeis4.)