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 *)
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
KEYWORD
nonn,easy
AUTHOR
STATUS
approved