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 A091870 A trinomial transform of Fibonacci(3n). 5
 0, 1, 8, 53, 336, 2105, 13144, 81997, 511392, 3189169, 19888040, 124023461, 773419248, 4823095913, 30077155576, 187563189565, 1169656805184, 7294059356257, 45486249993032, 283655347025429, 1768894026280080 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Binomial transform of A084326. Second binomial transform of A001076(n) = Fibonacci(3n)/2. LINKS Seiichi Manyama, Table of n, a(n) for n = 0..1258 S. Falcon, Iterated Binomial Transforms of the k-Fibonacci Sequence, British Journal of Mathematics & Computer Science, 4 (22): 2014. Index entries for linear recurrences with constant coefficients, signature (8,-11). FORMULA G.f.: x/(1 - 8*x + 11*x^2). a(n) = sqrt(5) * ((4+sqrt(5))^n - (4-sqrt(5))^n) / 10. a(n) = Sum_{i=0..n} Sum_{j=0..n} (n!/(i!*j!*(n-i-j)!)) * Fibonacci(3*i) / 2. MATHEMATICA LinearRecurrence[{8, -11}, {0, 1}, 30] (* G. C. Greubel, May 21 2019 *) CoefficientList[Series[x/(1 - 8 x + 11 x^2), {x, 0, 30}], x] (* Michael De Vlieger, Sep 22 2017 *) PROG (Sage) [lucas_number1(n, 8, 11) for n in range(0, 30)] # Zerinvary Lajos, Apr 23 2009 (PARI) my(x='x+O('x^30)); concat([0], Vec(x/(1 -8*x +11*x^2))) \\ G. C. Greubel, May 21 2019 (MAGMA) [n le 2 select n-1 else 8*Self(n-1) -11*Self(n-2): n in [1..30]]; // G. C. Greubel, May 21 2019 (GAP) a:=[0, 1];; for n in [3..30] do a[n]:=8*a[n-1]-11*a[n-2]; od; a; # G. C. Greubel, May 21 2019 CROSSREFS Cf. A084326. Sequence in context: A291662 A110099 A297334 * A252824 A054418 A293115 Adjacent sequences:  A091867 A091868 A091869 * A091871 A091872 A091873 KEYWORD nonn,easy AUTHOR Paul Barry, Feb 06 2004 STATUS approved

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Last modified April 10 20:35 EDT 2021. Contains 342856 sequences. (Running on oeis4.)