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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 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 October 16 23:50 EDT 2019. Contains 328103 sequences. (Running on oeis4.)