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A206423
Fibonacci sequence beginning 12, 7.
1
12, 7, 19, 26, 45, 71, 116, 187, 303, 490, 793, 1283, 2076, 3359, 5435, 8794, 14229, 23023, 37252, 60275, 97527, 157802, 255329, 413131, 668460, 1081591, 1750051, 2831642, 4581693, 7413335, 11995028, 19408363, 31403391, 50811754, 82215145, 133026899, 215242044
OFFSET
1,1
FORMULA
From Andrew Howroyd, Aug 28 2018: (Start)
a(n) = a(n-1) + a(n-2) for n > 2.
a(n) = 12*Fibonacci(n) - 5*Fibonacci(n-1).
G.f.: x*(12 - 5*x)/(1 - x - x^2).
(End)
MATHEMATICA
LinearRecurrence[{1, 1}, {12, 7}, 60]
PROG
(Magma) I:=[12, 7]; [n le 2 select I[n] else Self(n-1)+Self(n-2): n in [1..40]]; \\ Vincenzo Librandi, Feb 17 2012
(PARI) Vec((12 - 5*x)/(1 - x - x^2) + O(x^30)) \\ Andrew Howroyd, Aug 28 2018
(Python)
alst, terms = [12, 7], 37
[alst.append(alst[n-1] + alst[n-2]) for n in range(2, terms)]
print(alst) # Michael S. Branicky, Dec 07 2021
CROSSREFS
Cf. A000045.
Sequence in context: A359632 A364135 A305939 * A319406 A038333 A185259
KEYWORD
nonn
AUTHOR
STATUS
approved