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A049665 a(n) = (F(6*n+4) - 3)/4, where F=A000045 (the Fibonacci sequence). 1
0, 13, 246, 4427, 79452, 1425721, 25583538, 459077975, 8237820024, 147821682469, 2652552464430, 47598122677283, 854113655726676, 15326447680402897, 275021944591525482, 4935068554967055791, 88556212044815478768, 1589076748251711562045, 28514825256485992638054 (list; graph; refs; listen; history; text; internal format)
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

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Last modified August 19 20:20 EDT 2019. Contains 326133 sequences. (Running on oeis4.)