A049662 a(n) = (F(6*n+2)-1)/4, where F=A000045 (the Fibonacci sequence).

0, 5, 94, 1691, 30348, 544577, 9772042, 175352183, 3146567256, 56462858429, 1013184884470, 18180865062035, 326242386232164, 5854182087116921, 105049035181872418, 1885028451186586607, 33825463086176686512, 606973307099993770613, 10891694064713711184526

Offset

0,2

Links

Colin Barker, Table of n, a(n) for n = 0..700

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

Formula

G.f.: x*(-5+x) / ( (x-1)*(x^2-18*x+1) ). - R. J. Mathar, Oct 26 2015

From Colin Barker, Mar 04 2016: (Start)

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

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

Mathematica

LinearRecurrence[{19, -19, 1}, {0, 5, 94}, 20] (* Vincenzo Librandi, Mar 04 2016 *)
Table[(Fibonacci[6*n+2] - 1)/4, {n, 0, 30}] (* G. C. Greubel, Dec 02 2017 *)

Prog

(PARI) concat(0, Vec(x*(5-x)/((1-x)*(1-18*x+x^2)) + O(x^25))) \\ Colin Barker, Mar 04 2016
(PARI) a(n) = (fibonacci(6*n+2) - 1)/4; \\ Michel Marcus, Mar 04 2016
(Magma) [(Fibonacci(6*n+2)-1)/4: n in [0..30]]; // G. C. Greubel, Dec 02 2017

Crossrefs

Sequence in context: A015030 A270071 A047052 * A264176 A178018 A195854

Adjacent sequences: A049659 A049660 A049661 * A049663 A049664 A049665

Keyword

nonn,easy

Author

Clark Kimberling

Status

approved