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A091074 Fibonacci sequence beginning 12, 67. 2
12, 67, 79, 146, 225, 371, 596, 967, 1563, 2530, 4093, 6623, 10716, 17339, 28055, 45394, 73449, 118843, 192292, 311135, 503427, 814562, 1317989, 2132551, 3450540, 5583091, 9033631, 14616722, 23650353, 38267075, 61917428, 100184503 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

20 of the first 100 terms are prime numbers.

LINKS

Table of n, a(n) for n=1..32.

Tanya Khovanova, Recursive Sequences

Index entries for linear recurrences with constant coefficients, signature (1,1).

FORMULA

G.f.: (12*x+55*x^2)/(1-x-x^2). - Philippe Deléham, Nov 20 2008

a(n) = (61*sqrt(5)/5 + 6)*(1/2 + sqrt(5)/2)^n + (-61*sqrt(5)/5 + 6)*(1/2 - sqrt(5)/2)^n. - Antonio Alberto Olivares, May 23 2013

EXAMPLE

a(0) = (61*sqrt(5)/5 + 6)*(1/2 + sqrt(5)/2)^0 + (-61*sqrt(5)/5 + 6)*(1/2 - sqrt(5)/2)^0 =(61*sqrt(5)/5 + 6) + (-61*sqrt(5)/5 + 6) = 6 + 6 = 12.

MATHEMATICA

a={}; b=12; c=67; AppendTo[a, b]; AppendTo[a, c]; Do[b=b+c; AppendTo[a, b]; c=b+c; AppendTo[a, c], {n, 1, 12, 1}]; a (* Vladimir Joseph Stephan Orlovsky, Jul 23 2008 *)

LinearRecurrence[{1, 1}, {12, 67}, 50] (* or *) Rest[ CoefficientList[ Series[ (12x+55x^2)/(1-x-x^2), {x, 0, 50}], x]] (* Harvey P. Dale, May 11 2011 *)

PROG

(MAGMA) a0:=12; a1:=67; [GeneralizedFibonacciNumber(a0, a1, n): n in [0..35]]; // Vincenzo Librandi, Nov 02 2014

CROSSREFS

Sequence in context: A165107 A032167 A039925 * A212687 A117088 A199415

Adjacent sequences:  A091071 A091072 A091073 * A091075 A091076 A091077

KEYWORD

nonn,easy

AUTHOR

G. L. Honaker, Jr., Dec 17 2003

STATUS

approved

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Last modified August 20 11:27 EDT 2017. Contains 290835 sequences.