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A022120 Fibonacci sequence beginning 3, 7. 14
3, 7, 10, 17, 27, 44, 71, 115, 186, 301, 487, 788, 1275, 2063, 3338, 5401, 8739, 14140, 22879, 37019, 59898, 96917, 156815, 253732, 410547, 664279, 1074826, 1739105, 2813931, 4553036, 7366967, 11920003, 19286970, 31206973, 50493943, 81700916, 132194859 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,1
COMMENTS
From Greg Dresden, Feb 18 2022: (Start)
a(n) is also the number of ways to tile this figure, with two cells on the top row and n+1 cells on the bottom row, using squares and dominoes. Shown here are the figures for a(0) through a(4):
.___ .___ .___ .___ .___
|_|_| |_|_| |_|_|_ |_|_|___ |_|_|_____
|_| |_|_| |_|_|_| |_|_|_|_| |_|_|_|_|_|
(End)
LINKS
Tanya Khovanova, Recursive Sequences
FORMULA
G.f.: (3+4x)/(1-x-x^2). - Philippe Deléham, Nov 19 2008
a(n) = 4*Fibonacci(n+2) - Fibonacci(n+1). - Gary Detlefs, Dec 21 2010
a(n) = round(((15+11*sqrt(5))/10)*((1+sqrt(5))/2)^n + ((15-11*sqrt(5))/10)*((1-sqrt(5))/2)^n). - Bogart B. Strauss, Oct 27 2013
a(n) = Lucas(n+3) - Fibonacci(n-1). - Greg Dresden, Sam Neale, and Kyle Wood, Feb 18 2022
E.g.f.: exp(x/2)*(15*cosh(sqrt(5)*x/2) + 11*sqrt(5)*sinh(sqrt(5)*x/2))/5. - Stefano Spezia, Jul 26 2022
MATHEMATICA
Table[4*Fibonacci[n+2]-Fibonacci[n+1], {n, 0, 30}] (* Zak Seidov, Mar 15 2011 *)
LinearRecurrence[{1, 1}, {3, 7}, 50] (* Harvey P. Dale, May 28 2024 *)
PROG
(PARI) v=vector(100); v[1]=3; v[2]=7; for(i=3, #v, v[i]=v[i-2]+v[i-1]); v \\ Charles R Greathouse IV, Mar 15 2011
CROSSREFS
Cf. A000032.
Sequence in context: A217258 A258864 A111244 * A041191 A304216 A305247
KEYWORD
nonn,easy
AUTHOR
STATUS
approved

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Last modified June 23 16:55 EDT 2024. Contains 373653 sequences. (Running on oeis4.)