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A049662
a(n) = (F(6*n+2)-1)/4, where F=A000045 (the Fibonacci sequence).
1
0, 5, 94, 1691, 30348, 544577, 9772042, 175352183, 3146567256, 56462858429, 1013184884470, 18180865062035, 326242386232164, 5854182087116921, 105049035181872418, 1885028451186586607, 33825463086176686512, 606973307099993770613, 10891694064713711184526
OFFSET
0,2
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
KEYWORD
nonn,easy
STATUS
approved