A022120 Fibonacci sequence beginning 3, 7.

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

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

Michael De Vlieger, Table of n, a(n) for n = 0..4782

Tanya Khovanova, Recursive Sequences

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

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 *)

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

Adjacent sequences: A022117 A022118 A022119 * A022121 A022122 A022123

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved