A049663 a(n) = (F(6*n+5) - 1)/4, where F=A000045 (the Fibonacci sequence).

1, 22, 399, 7164, 128557, 2306866, 41395035, 742803768, 13329072793, 239180506510, 4291920044391, 77015380292532, 1381984925221189, 24798713273688874, 444994854001178547, 7985108658747524976, 143286961003454271025, 2571180189403429353478

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.: (1+3*x)/( (1-x)*(x^2-18*x+1) ). - R. J. Mathar, Oct 26 2015

a(n) = A049664(n+1) + 3*A049664(n). - R. J. Mathar, Oct 26 2015

From Colin Barker, Mar 04 2016: (Start)

a(n) = (-1/4+1/40*(9+4*sqrt(5))^(-n)*(25-11*sqrt(5)+(9+4*sqrt(5))^(2*n)*(25+11*sqrt(5)))).

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

Mathematica

(Fibonacci[6*Range[0, 20]+5]-1)/4 (* or *) LinearRecurrence[{19, -19, 1}, {1, 22, 399}, 20] (* Harvey P. Dale, Sep 22 2016 *)

Prog

(PARI) Vec((1+3*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+5) - 1)/4, ", ")) \\ G. C. Greubel, Dec 02 2017
(Magma) [(Fibonacci(6*n+5) - 1)/4: n in [0..30]]; // G. C. Greubel, Dec 02 2017

Crossrefs

Sequence in context: A264464 A268947 A159761 * A246645 A183539 A269540

Adjacent sequences: A049660 A049661 A049662 * A049664 A049665 A049666

Keyword

nonn,easy

Author

Clark Kimberling

Status

approved