OFFSET
0,1
COMMENTS
a(n) is the minimum number of nodes required for a full binary AVL tree of height n+1 whose root node has a balance factor of 0. - Sumukh Patel, Jun 24 2022
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (2,0,-1).
FORMULA
From R. J. Mathar, May 28 2008: (Start)
a(n) = A022403(n+1).
O.g.f.: (3+x-3*x^2)/((1-x)*(1-x-x^2)).
a(n+1) - a(n) = A022087(n+1).
(End)
a(n) = (2^(-n)*(-5*2^n + (10-6*sqrt(5))*(1-sqrt(5))^n + 2*(1+sqrt(5))^n*(5+3*sqrt(5)))) / 5. - Colin Barker, Mar 02 2018
MATHEMATICA
Table[4*Fibonacci[n + 2] - 1, {n, 0, 100}] (* Vladimir Joseph Stephan Orlovsky, Jun 28 2011 *)
CoefficientList[Series[(3+x-3*x^2)/((1-x)*(1-x-x^2)), {x, 0, 50}], x] (* G. C. Greubel, Mar 01 2018 *)
PROG
(PARI) for(n=0, 40, print1(4*fibonacci(n+2) -1, ", ")) \\ G. C. Greubel, Mar 01 2018
(Magma) [4*Fibonacci(n+2) - 1: n i [0..40]]; // G. C. Greubel, Mar 01 2018
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved