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

0,1

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).

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

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 *)

Prog

(PARI) Vec((4+10*x)/(1-x-x^2)+O(x^99)) \\ Charles R Greathouse IV, May 15 2013
(Magma) [4*Fibonacci(n+2) + 6*Fibonacci(n): n in [0..40]]; // G. C. Greubel, Mar 06 2018

Crossrefs

Cf. A000045, A022113.

Sequence in context: A011859 A032825 A251966 * A336634 A045248 A271375

Adjacent sequences: A022380 A022381 A022382 * A022384 A022385 A022386

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

More terms from Stefan Steinerberger, Apr 08 2006

Status

approved