A022383 Fibonacci sequence beginning 4, 14.

4, 14, 18, 32, 50, 82, 132, 214, 346, 560, 906, 1466, 2372, 3838, 6210, 10048, 16258, 26306, 42564, 68870, 111434, 180304, 291738, 472042, 763780, 1235822, 1999602, 3235424, 5235026, 8470450, 13705476, 22175926, 35881402, 58057328, 93938730

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

• Harvey P. Dale, 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

Cf. A000045, A022113.

Programs

Magma

[4*Fibonacci(n+2) + 6*Fibonacci(n): n in [0..40]]; // G. C. Greubel, Mar 06 2018

Mathematica

a[1] := 4; a[2] := 14; a[n_] := a[n - 1] + a[n - 2]; Table[a[n], {n, 1, 30}] (* Stefan Steinerberger, Apr 08 2006 *)
LinearRecurrence[{1,1},{4,14},40] (* Harvey P. Dale, Feb 15 2015 *)

PARI

Vec((4+10*x)/(1-x-x^2)+O(x^99)) \\ Charles R Greathouse IV, May 15 2013

Formula

G.f.: (4+10*x)/(1-x-x^2). - Philippe Deléham, Nov 19 2008

a(n) = 4*Fibonacci(n+2) + 6*Fibonacci(n) = 4*Fibonacci(n) + 14*Fibonacci(n-1). - G. C. Greubel, Mar 06 2018

E.g.f.: 4*exp(x/2)*(5*cosh(sqrt(5)*x/2) + 6*sqrt(5)*sinh(sqrt(5)*x/2))/5. - Stefano Spezia, Jul 17 2022

a(n) = 2 * A022113(n). - Alois P. Heinz, Jul 17 2022

Extensions

More terms from Stefan Steinerberger, Apr 08 2006