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A049663 a(n) = (F(6*n+5) - 1)/4, where F=A000045 (the Fibonacci sequence). 1
1, 22, 399, 7164, 128557, 2306866, 41395035, 742803768, 13329072793, 239180506510, 4291920044391, 77015380292532, 1381984925221189, 24798713273688874, 444994854001178547, 7985108658747524976, 143286961003454271025, 2571180189403429353478 (list; graph; refs; listen; history; text; internal format)
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

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Last modified November 13 00:25 EST 2019. Contains 329083 sequences. (Running on oeis4.)