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A104449
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Fibonacci-type sequence. Each term is the sum of the two previous terms.
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4
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3, 1, 4, 5, 9, 14, 23, 37, 60, 97, 157, 254, 411, 665, 1076, 1741, 2817, 4558, 7375, 11933, 19308, 31241, 50549, 81790, 132339, 214129, 346468, 560597, 907065, 1467662, 2374727, 3842389, 6217116, 10059505, 16276621, 26336126, 42612747, 68948873, 111561620
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OFFSET
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0,1
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COMMENTS
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The 6th row in the Wythoff array begins with the 6th term of the sequence (14, 23, 37, 60, 97, 157,...). a(n) = f(n-3) + f(n+2) for the Fibonacci numbers f(n) = f(n-1) + f(n-2); f(0) = 0, f(1) = 1.
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REFERENCES
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V. E. Hoggatt, Jr., Fibonacci and Lucas Numbers. Houghton, Boston, MA, 1969.
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LINKS
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Table of n, a(n) for n=0..38.
Tanya Khovanova, Recursive Sequences
R. Knott, Fibonacci Numbers and the Golden Section .
Eric Weisstein's World of Mathematics, Fibonacci Number
Index entries for sequences related to linear recurrences with constant coefficients, signature (1,1).
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FORMULA
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a(n) = a(n-1) + a(n-2); a(0) = 3, a(1) = 1
a(n)=3*fibonacci(n-1)+fibonacci(n), n>=0. - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Oct 05 2007
G.f.: (3-2x)/(1-x-x^2). [From Philippe DELEHAM, Nov 19 2008]
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MAPLE
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a:=n->3*fibonacci(n-1)+fibonacci(n): seq(a(n), n=0..32); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Oct 05 2007
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MATHEMATICA
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Join[{a=3, b=1}, Table[c=a+b; a=b; b=c, {n, 0, 60}]] [From Vladimir Joseph Stephan Orlovsky, 22 Nov 2010]
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PROG
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(PARI) a(n)=3*fibonacci(n-1)+fibonacci(n) \\ Charles R Greathouse IV, Jun 05, 2011
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CROSSREFS
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Cf. Other Fibonacci-type sequences: A000045, A000032, A013655. Other related sequences: A103343, A103344. Wythoff array: A035513.
Essentially the same as A000285.
Sequence in context: A183904 A105177 A050057 * A116416 A051203 A194540
Adjacent sequences: A104446 A104447 A104448 * A104450 A104451 A104452
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KEYWORD
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nonn,easy,changed
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AUTHOR
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Casey Mongoven, Mar 08 2005
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STATUS
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approved
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