A022407 a(n) = a(n-1) + a(n-2) + 1, with a(0)=3, a(1)=8.

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

Author

N. J. A. Sloane

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (2,0,-1)

Programs

Magma

[Fibonacci(n-2) + Fibonacci(n+5) - 1: n in [0..30]]; // G. C. Greubel, Mar 01 2018

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 *)

PARI

for(n=0,30, print1(fibonacci(n-2) + fibonacci(n+5) - 1, ", ")) \\ G. C. Greubel, Mar 01 2018

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)

Extensions

More terms from James Sellers, Aug 08 2000