OFFSET
2,1
COMMENTS
This sequence is associated with A340131, whose terms are sorted by the length of their ternary code. Elements with the same length of ternary code form a range that has a maximum. The maximal term of the n-range (a set of elements with ternary code length n in A340131) is a(n). Example: numbers 29, 33, 44, 45 and 50 have a ternary length of 4 (see A340131), respectively a(4) = 50.
Ternary code for a(n) is 12..12 for even n and 12..120 for odd n.
LINKS
Andrew Howroyd, Table of n, a(n) for n = 2..1000
Gennady Eremin, Arithmetization of well-formed parenthesis strings. Motzkin Numbers of the Second Kind, arXiv:2012.12675 [math.CO], 2020.
Index entries for linear recurrences with constant coefficients, signature (3,1,-3).
FORMULA
a(n) = 5*3^(n-2*k)*(9^k-1)/8 where k = floor(n/2).
a(n+1) = 3*a(n) for even n >= 2; a(n+1) = 3*a(n)+5 for odd n >= 3.
a(n) = 5*A033113(n-1).
a(n) = (5/8)*(3^n - (-1)^(n-1) - 2).
a(n) = 2*a(n-1) + 3*a(n-2) + 5 for n > 3.
From Stefano Spezia, Jan 06 2021: (Start)
G.f.: 5*x^2/(1 - 3*x - x^2 + 3*x^3).
a(n) = 3*a(n-1) + a(n-2) - 3*a(n-3) for n > 4. (End)
PROG
(PARI) Vec(5/(1 - 3*x - x^2 + 3*x^3) + O(x^30)) \\ Andrew Howroyd, Jan 08 2021
CROSSREFS
KEYWORD
nonn,easy,base
AUTHOR
Gennady Eremin, Jan 06 2021
STATUS
approved