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

%I A017617 #56 Apr 04 2025 23:42:37
%S A017617 8,20,32,44,56,68,80,92,104,116,128,140,152,164,176,188,200,212,224,
%T A017617 236,248,260,272,284,296,308,320,332,344,356,368,380,392,404,416,428,
%U A017617 440,452,464,476,488,500,512,524,536,548,560,572,584,596,608,620,632,644,656
%N A017617 a(n) = 12*n + 8.
%C A017617 Also the number of cube units that frame a cube of edge length n+1. - _Peter M. Chema_, Mar 27 2016
%H A017617 Vincenzo Librandi, <a href="/A017617/b017617.txt">Table of n, a(n) for n = 0..3000</a>
%H A017617 Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/RecursiveSequences.html">Recursive Sequences</a>.
%H A017617 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1).
%F A017617 a(n) = 2*a(n-1) - a(n-2). - _Vincenzo Librandi_, Jun 08 2011
%F A017617 A089911(a(n)) = 9. - _Reinhard Zumkeller_, Jul 05 2013
%F A017617 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
%F A017617 Sum_{n>=0} (-1)^n/a(n) = sqrt(3)*Pi/36 - log(2)/12. - _Amiram Eldar_, Dec 12 2021
%F A017617 From _Elmo R. Oliveira_, Apr 04 2025: (Start)
%F A017617 E.g.f.: 4*exp(x)*(2 + 3*x).
%F A017617 a(n) = 4*A016789(n) = 2*A016957(n) = A016933(2*n+1). (End)
%e A017617 For n=3; a(3)= 12*3 + 8 = 44.
%e A017617 Thus, there are 44 cube units that frame a cube of edge length 4. - _Peter M. Chema_, Mar 26 2016
%t A017617 12*Range[0,200]+8 (* _Vladimir Joseph Stephan Orlovsky_, Feb 19 2011 *)
%o A017617 (Magma) [12*n+8: n in [0..60]]; // _Vincenzo Librandi_, Jun 08 2011
%o A017617 (Haskell)
%o A017617 a017617 = (+ 8) . (* 12)  -- _Reinhard Zumkeller_, Jul 05 2013
%o A017617 (PARI) my(x='x+O('x^99)); Vec(4*(2+x)/(1-x)^2) \\ _Altug Alkan_, Mar 27 2016
%Y A017617 Cf. A008594, A016789, A016933, A016957, A017533, A017545, A089911.
%K A017617 nonn,easy
%O A017617 0,1
%A A017617 _N. J. A. Sloane_