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A022383
Fibonacci sequence beginning 4, 14.
3
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
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
Sequence in context: A011859 A032825 A251966 * A336634 A045248 A271375
KEYWORD
nonn,easy
EXTENSIONS
More terms from Stefan Steinerberger, Apr 08 2006
STATUS
approved