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A104449 Fibonacci-type sequence. Each term is the sum of the two previous terms. 5
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

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.

REFERENCES

V. E. Hoggatt, Jr., Fibonacci and Lucas Numbers. Houghton, Boston, MA, 1969.

LINKS

Table of n, a(n) for n=0..38.

Tanya Khovanova, Recursive Sequences

Ron Knott, Fibonacci Numbers and the Golden Section .

Eric Weisstein's World of Mathematics, Fibonacci Number

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

FORMULA

a(n) = a(n-1) + a(n-2); a(0) = 3, a(1) = 1

a(n) = 3*fibonacci(n-1) + fibonacci(n). - Zerinvary Lajos, Oct 05 2007

G.f.: (3-2x)/(1-x-x^2). - Philippe Deléham, Nov 19 2008

a(n) = ((3*sqrt(5)-1)(((1+sqrt(5))/2)^n) + (3*sqrt(5)+1)(((1-sqrt(5))/2)^n))/(2*sqrt(5)). - Bogart B. Strauss, Jul 19 2013

MAPLE

a:=n->3*fibonacci(n-1)+fibonacci(n): seq(a(n), n=0..32); # Zerinvary Lajos, Oct 05 2007

MATHEMATICA

Join[{a=3, b=1}, Table[c=a+b; a=b; b=c, {n, 0, 60}]] (* Vladimir Joseph Stephan Orlovsky, Nov 22 2010 *)

LinearRecurrence[{1, 1}, {3, 1}, 40] (* Harvey P. Dale, May 23 2014 *)

PROG

(PARI) a(n)=3*fibonacci(n-1)+fibonacci(n) \\ Charles R Greathouse IV, Jun 05 2011

CROSSREFS

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 A243553

Adjacent sequences:  A104446 A104447 A104448 * A104450 A104451 A104452

KEYWORD

nonn,easy

AUTHOR

Casey Mongoven, Mar 08 2005

STATUS

approved

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Last modified March 24 07:54 EDT 2017. Contains 283985 sequences.