A049665 a(n) = (F(6*n+4) - 3)/4, where F=A000045 (the Fibonacci sequence).

0, 13, 246, 4427, 79452, 1425721, 25583538, 459077975, 8237820024, 147821682469, 2652552464430, 47598122677283, 854113655726676, 15326447680402897, 275021944591525482, 4935068554967055791, 88556212044815478768, 1589076748251711562045, 28514825256485992638054

Offset

0,2

Links

Colin Barker, Table of n, a(n) for n = 0..797

Index entries for linear recurrences with constant coefficients, signature (19,-19,1).

Formula

G.f.: x*(-13+x) / ( (x-1)*(x^2-18*x+1) ). - R. J. Mathar, Oct 26 2015

From Colin Barker, Mar 04 2016: (Start)

a(n) = (-3/4+1/40*(9+4*sqrt(5))^(-n)*(15-7*sqrt(5)+(9+4*sqrt(5))^(2*n)*(15+7*sqrt(5)))).

a(n) = 19*a(n-1) - 19*a(n-2) + a(n-3) for n>2. (End)

Mathematica

LinearRecurrence[{19, -19, 1}, {0, 13, 246}, 20] (* Vincenzo Librandi, Mar 04 2016 *)
Table[(Fibonacci[6*n+4] - 3)/4, {n, 0, 30}] (* G. C. Greubel, Dec 02 2017 *)

Prog

(PARI) concat(0, Vec(x*(13-x)/((1-x)*(1-18*x+x^2)) + O(x^25))) \\ Colin Barker, Mar 04 2016
(PARI) for(n=0, 30, print1((fibonacci(6*n+4) - 3)/4, ", ")) \\ G. C. Greubel, Dec 02 2017
(Magma) [(Fibonacci(6*n+4) - 3)/4: n in [0..30]]; // G. C. Greubel, Dec 02 2017

Crossrefs

Sequence in context: A020520 A259420 A203156 * A196665 A027400 A053100

Adjacent sequences: A049662 A049663 A049664 * A049666 A049667 A049668

Keyword

nonn,easy

Author

Clark Kimberling

Status

approved