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A022407
a(n) = a(n-1) + a(n-2) + 1, with a(0)=3, a(1)=8.
2
3, 8, 12, 21, 34, 56, 91, 148, 240, 389, 630, 1020, 1651, 2672, 4324, 6997, 11322, 18320, 29643, 47964, 77608, 125573, 203182, 328756, 531939, 860696, 1392636, 2253333, 3645970, 5899304, 9545275, 15444580, 24989856, 40434437, 65424294
OFFSET
0,1
FORMULA
a(n) = Fibonacci(n-2) + Fibonacci(n+5) - 1. - Zerinvary Lajos, Feb 01 2008
From Lambert Herrgesell (zero815(AT)googlemail.com), Feb 24 2008: (Start)
O.g.f.: (-4*x^2 + 2*x + 3)/(x^3 - 2*x + 1).
a(n) = -1 - B*(2/(-1-sqrt(5)))^n - C*(2/(-1+sqrt(5)))^n, with B=(-8 - 6*sqrt(5))/(5 + 3*sqrt(5)), C=(-8 + 6*sqrt(5))/(5 - 3*sqrt(5)). (End)
MAPLE
with(combinat): seq(fibonacci(n-2)+fibonacci(n+5)-1, n=0..32); # Zerinvary Lajos, Feb 01 2008
MATHEMATICA
Transpose[NestList[{#[[2]], Total[#]+1}&, {3, 8}, 35]][[1]] (* Harvey P. Dale, Feb 07 2011 *)
Table[Fibonacci[n-2] + Fibonacci[n+5] - 1, {n, 0, 50}] (* G. C. Greubel, Mar 01 2018 *)
PROG
(PARI) for(n=0, 30, print1(fibonacci(n-2) + fibonacci(n+5) - 1, ", ")) \\ G. C. Greubel, Mar 01 2018
(Magma) [Fibonacci(n-2) + Fibonacci(n+5) - 1: n in [0..30]]; // G. C. Greubel, Mar 01 2018
CROSSREFS
Sequence in context: A014255 A350221 A370755 * A330897 A169923 A158022
KEYWORD
nonn
EXTENSIONS
More terms from James A. Sellers, Aug 08 2000
STATUS
approved