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 A083582 a(n) = (8*2^n-5*(-1)^n)/3. 6
 1, 7, 9, 23, 41, 87, 169, 343, 681, 1367, 2729, 5463, 10921, 21847, 43689, 87383, 174761, 349527, 699049, 1398103, 2796201, 5592407, 11184809, 22369623, 44739241, 89478487, 178956969, 357913943, 715827881, 1431655767, 2863311529 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Binomial transform of A083581. LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (1,2). FORMULA a(n) = (8*2^n-5(-1)^n)/3. G.f.: (1+6*x)/((1-2*x)*(1+x)). E.g.f.: (8*exp(2*x)-5*exp(-x))/3. a(n) = 6*A001045(n) + A001045(n+1). - Creighton Dement, Mar 25 2005 a(n) = 2^(n+2)th coefficient of - eta(z)^3 eta(z^5) eta(z^10)^2 /eta(z^2)^2. - Kok Seng Chua (chuaks(AT)ihpc.a-star.edu.sg), Aug 30 2005 a(n) = a(n-1)+2*a(n-2). a(n)+a(n+1) = 8*A000079 = a(n+2)-a(n). - Paul Curtz, Jul 27 2008 MAPLE BB := n->if n=1 then 3; > elif n=2 then 1; > else 2*BB(n-2)+BB(n-1); > fi: > L:=[]: for k from 2 to 32 do L:=[op(L), BB(k)]: od: L; # Zerinvary Lajos, Mar 19 2007 MATHEMATICA f[n_]:=2/(n+1); x=6; Table[x=f[x]; Denominator[x], {n, 0, 5!}] (* Vladimir Joseph Stephan Orlovsky, Mar 12 2010 *) LinearRecurrence[{1, 2}, {1, 7}, 40] (* Harvey P. Dale, May 28 2017 *) PROG (Magma) [(8*2^n-5*(-1)^n)/3: n in [0..30]]; // Vincenzo Librandi, Aug 13 2011 (PARI) a(n)=(8*2^n-5*(-1)^n)/3 \\ Charles R Greathouse IV, Oct 07 2015 CROSSREFS Cf. A140966. Sequence in context: A350540 A179788 A319878 * A229500 A303188 A029633 Adjacent sequences: A083579 A083580 A083581 * A083583 A083584 A083585 KEYWORD easy,nonn AUTHOR Paul Barry, May 01 2003 STATUS approved

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Last modified September 30 02:39 EDT 2023. Contains 365781 sequences. (Running on oeis4.)