A017617 a(n) = 12*n + 8.

8, 20, 32, 44, 56, 68, 80, 92, 104, 116, 128, 140, 152, 164, 176, 188, 200, 212, 224, 236, 248, 260, 272, 284, 296, 308, 320, 332, 344, 356, 368, 380, 392, 404, 416, 428, 440, 452, 464, 476, 488, 500, 512, 524, 536, 548, 560, 572, 584, 596, 608, 620, 632

Offset

0,1

Comments

Also the number of cube units that frame a cube of edge length n+1. Peter M. Chema, Mar 27 2016

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..3000

Tanya Khovanova, Recursive Sequences.

Index entries for linear recurrences with constant coefficients, signature (2,-1).

Formula

a(n) = 2*a(n-1) - a(n-2). - Vincenzo Librandi, Jun 08 2011

A089911(a(n)) = 9. - Reinhard Zumkeller, Jul 05 2013

G.f.: 12*x/(1-x)^2 + 8/(1-x) = 4*(2+x)/(1-x)^2. (see the PARI program). - Wolfdieter Lang, Oct 11 2021

Sum_{n>=0} (-1)^n/a(n) = sqrt(3)*Pi/36 - log(2)/12. - Amiram Eldar, Dec 12 2021

Example

For n=3; a(3)= 12*3+8 = 44.
Thus, there are 44 cube units that frame a cube of edge length 4. - Peter M. Chema, Mar 26 2016

Mathematica

12*Range[0, 200]+8 (* Vladimir Joseph Stephan Orlovsky, Feb 19 2011 *)

Prog

(Magma) [12*n+8: n in [0..60]]; // Vincenzo Librandi, Jun 08 2011
(Haskell)
a017617 = (+ 8) . (* 12)  -- Reinhard Zumkeller, Jul 05 2013
(PARI) x='x+O('x^99); Vec(4*(2+x)/(1-x)^2) \\ Altug Alkan, Mar 27 2016

Crossrefs

Cf. A008594, A017533, A017545, A016957, A016789, A089911.

Sequence in context: A365145 A194218 A339273 * A246309 A363518 A038522

Adjacent sequences: A017614 A017615 A017616 * A017618 A017619 A017620

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved