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
KEYWORD
nonn,easy
AUTHOR
STATUS
approved