A340395 a(n) = A340131(A001006(n)).

5, 15, 50, 150, 455, 1365, 4100, 12300, 36905, 110715, 332150, 996450, 2989355, 8968065, 26904200, 80712600, 242137805, 726413415, 2179240250, 6537720750, 19613162255, 58839486765, 176518460300, 529555380900, 1588666142705, 4765998428115, 14297995284350

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)

Example

A001006(2) = 2, so a(2) = A340131(2) = 5.
A001006(3) = 4, so a(3) = A340131(4) = 15, etc.

Prog

(PARI) Vec(5/(1 - 3*x - x^2 + 3*x^3) + O(x^30)) \\ Andrew Howroyd, Jan 08 2021

Crossrefs

Subsequence of A340131.

Sequence in context: A152809 A344204 A034539 * A029609 A014274 A363510

Adjacent sequences: A340392 A340393 A340394 * A340396 A340397 A340398

Keyword

nonn,easy,base

Author

Gennady Eremin, Jan 06 2021

Status

approved