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A017617
a(n) = 12*n + 8.
13
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
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
KEYWORD
nonn,easy
STATUS
approved