A022359 Fibonacci sequence beginning 0, 25.

0, 25, 25, 50, 75, 125, 200, 325, 525, 850, 1375, 2225, 3600, 5825, 9425, 15250, 24675, 39925, 64600, 104525, 169125, 273650, 442775, 716425, 1159200, 1875625, 3034825, 4910450, 7945275, 12855725, 20801000, 33656725, 54457725, 88114450, 142572175, 230686625

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

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

Programs

Magma

[Lucas(n+5)+Lucas(n-5): n in [0..40]]; // Bruno Berselli, Dec 27 2016

Mathematica

LinearRecurrence[{1, 1}, {0, 25}, 30] (* or *) Table[(-25/2)(Fibonacci[n] - LucasL[n]), {n, 50}] (* Harvey P. Dale, Nov 22 2012 *)

PARI

for(n=0,50, print1(25*fibonacci(n), ", ")) \\ G. C. Greubel, Aug 26 2017

Formula

G.f.: 25*x/(1 - x - x^2). - Philippe Deléham, Nov 20 2008

a(n) = (-25/2)*(Fibonacci(n) - Lucas(n)). - Harvey P. Dale, Nov 22 2012

a(n) = Lucas(n+5) + Lucas(n-5), with Lucas(-i) = (-1)^i*Lucas(i) for the negative indices. - Bruno Berselli, Dec 27 2016