A022387 Fibonacci sequence beginning 4, 30.

4, 30, 34, 64, 98, 162, 260, 422, 682, 1104, 1786, 2890, 4676, 7566, 12242, 19808, 32050, 51858, 83908, 135766, 219674, 355440, 575114, 930554, 1505668, 2436222, 3941890, 6378112, 10320002, 16698114, 27018116, 43716230, 70734346, 114450576, 185184922, 299635498, 484820420

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

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

Crossrefs

Equals 2 * A022117.

Programs

GAP

List([0..40],n->4*Fibonacci(n+2)+22*Fibonacci(n)); # Muniru A Asiru, Mar 03 2018

Magma

I:=[4,30]; [n le 2 select I[n] else Self(n-1) + Self(n-2): n in [1..40]]; // Vincenzo Librandi, Oct 17 2012

Magma

[4*Fibonacci(n+2) + 22*Fibonacci(n): n in [0..40]]; // G. C. Greubel, Mar 01 2018

Maple

with(combinat,fibonacci):  seq(4*fibonacci(n+2)+22*fibonacci(n),n=0..35); # Muniru A Asiru, Mar 03 2018

Mathematica

LinearRecurrence[{1, 1}, {4, 30}, 30] (* Harvey P. Dale, Oct 16 2012 *)
CoefficientList[Series[(4 + 26 * x)/(1 - x - x^2), {x, 0, 30}], x] (* Vincenzo Librandi, Oct 17 2012 *)
Table[4 * Fibonacci[n + 2] + 22 * Fibonacci[n], {n, 0, 50}] (* G. C. Greubel, Mar 02 2018 *)

PARI

for(n=0, 40, print1(4*fibonacci(n+2) + 22*fibonacci(n), ", ")) \\ G. C. Greubel, Mar 01 2018

Formula

G.f.: (4+26*x)/(1-x-x^2). - Philippe Deléham, Nov 19 2008

a(n) = 4*Fibonacci(n+2) + 22*fibonacci(n) = 4*Fibonacci(n-1) + 30*Fibonacci(n). - G. C. Greubel, Mar 02 2018