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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
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
KEYWORD
nonn,easy
AUTHOR
STATUS
approved

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Last modified July 14 05:06 EDT 2024. Contains 374291 sequences. (Running on oeis4.)