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 A122069 a(n) = 3*a(n-1) + 9*a(n-2) for n > 1, with a(0)=1, a(1)=3. 3
 1, 3, 18, 81, 405, 1944, 9477, 45927, 223074, 1082565, 5255361, 25509168, 123825753, 601059771, 2917611090, 14162371209, 68745613437, 333698181192, 1619805064509, 7862698824255, 38166342053346, 185263315578333 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS G. C. Greubel, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (3,9). FORMULA a(n) = 3^n*Fibonacci(n+1) = 3^n*A000045(n+1). a(n) = Sum_{k=0..n} 2^k*A016095(n,k). G.f.: 1/(1-3*x-9*x^2). a(n+1)/a(n) -> 3*((1+sqrt(5))/2 if n ->infinity. a(n) = A099012(n+1). - R. J. Mathar, Aug 02 2008 a(n) = (1/2)*((3/2)+(3/2)*sqrt(5))^n+(1/10)*((3/2)+(3/2)*sqrt(5))^n*sqrt(5)-(1/10)*sqrt(5)*((3/2)-(3/2)*sqrt(5))^n+(1/2)*((3/2)-(3/2)*sqrt(5))^n, with n >= 0. - Paolo P. Lava, Nov 19 2008 a(n) = A085504(n) for n >= 2. - Georg Fischer, Nov 03 2018 MAPLE with(combinat); seq(3^n*fibonacci(n+1), n=0..25); # G. C. Greubel, Oct 03 2019 MATHEMATICA Table[3^n*Fibonacci[n+1], {n, 0, 25}] (* G. C. Greubel, Oct 03 2019 *) LinearRecurrence[{3, 9}, {1, 3}, 30] (* Harvey P. Dale, Apr 28 2020 *) PROG (Sage) [lucas_number1(n, 3, -9) for n in range(1, 23)] # Zerinvary Lajos, Apr 22 2009 (PARI) vector(26, n, 3^(n-1)*fibonacci(n) ) \\ G. C. Greubel, Oct 03 2019 (MAGMA) [3^n*Fibonacci(n+1): n in [0..25]]; // G. C. Greubel, Oct 03 2019 (GAP) List([0..25], n-> 3^n*Fibonacci(n+1) ); # G. C. Greubel, Oct 03 2019 CROSSREFS Third row of A234357. Cf. A000045, A085504, A099012. Sequence in context: A036290 A078904 A099012 * A103897 A119424 A301996 Adjacent sequences:  A122066 A122067 A122068 * A122070 A122071 A122072 KEYWORD nonn,easy AUTHOR Philippe Deléham, Oct 15 2006 EXTENSIONS Corrected by T. D. Noe, Nov 07 2006 STATUS approved

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Last modified September 26 13:34 EDT 2021. Contains 347668 sequences. (Running on oeis4.)