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A022407 a(n)=a(n-1)+a(n-2)+1. 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

LINKS

Table of n, a(n) for n=0..34.

Index entries for linear recurrences with constant coefficients, signature (2,0,-1)

FORMULA

a(n)=Fibonacci(n)+Fibonacci(n+7)-1, n>=-2 - Zerinvary Lajos, Feb 01 2008

O.g.f.: (-4*x^2 + 2*x + 3)/(x^3 - 2*x + 1) so with B=(-8 - 6*sqrt(5))/(5 + 3*sqrt(5)), C=(-8 + 6*sqrt(5))/(5 - 3*sqrt(5)), a(n) = -1 - B*(2/(-1-sqrt(5)))^n - C*(2/(-1+sqrt(5)))^n - Lambert Herrgesell (zero815(AT)googlemail.com), Feb 24 2008

MAPLE

with(combinat): seq(fibonacci(n)+fibonacci(n+7)-1, n=-2..32); - Zerinvary Lajos, Feb 01 2008

MATHEMATICA

Transpose[NestList[{#[[2]], Total[#]+1}&, {3, 8}, 35]][[1]]  (* Harvey P. Dale, Feb 07 2011 *)

CROSSREFS

Sequence in context: A086813 A103888 A014255 * A169923 A158022 A209934

Adjacent sequences:  A022404 A022405 A022406 * A022408 A022409 A022410

KEYWORD

nonn

AUTHOR

N. J. A. Sloane.

EXTENSIONS

More terms from James A. Sellers, Aug 08 2000

STATUS

approved

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Last modified December 2 17:11 EST 2016. Contains 278679 sequences.