A080675 a(n) = (5*4^n - 8)/6.

2, 12, 52, 212, 852, 3412, 13652, 54612, 218452, 873812, 3495252, 13981012, 55924052, 223696212, 894784852, 3579139412, 14316557652, 57266230612, 229064922452, 916259689812, 3665038759252, 14660155037012, 58640620148052, 234562480592212, 938249922368852

Offset: 1

Author

N. J. A. Sloane, Mar 02 2003

Keywords

• nonn
• easy

Comments

These numbers have a simple binary pattern: 10,1100,110100,11010100,1101010100, ... i.e., the n-th term has a binary expansion 1(10){n-1}0, that is, there are n-1 10's between the most significant 1 and the least significant 0.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..170
• Andrei Asinowski, Cyril Banderier, Benjamin Hackl, On extremal cases of pop-stack sorting, Permutation Patterns (Zürich, Switzerland, 2019).
• Index entries for linear recurrences with constant coefficients, signature (5,-4).

Crossrefs

a(n) = A072197(n-1) - 1 = A014486(|A106191(n)|). a(n) = A079946(A020988(n-2)) for n>=2. Cf. also A122229.

Programs

Magma

[(5*4^n-8)/6: n in [1..40] ]; // Vincenzo Librandi, Apr 28 2011

Mathematica

(5*4^Range[30]-8)/6 (* or *) LinearRecurrence[{5,-4},{2,12},30] (* Harvey P. Dale, Oct 16 2012 *)

PARI

a(n)=(5*4^n-8)/6 \\ Charles R Greathouse IV, Oct 07 2015

Formula

a(1)=2, a(2)=12, a(n)=5*a(n-1)-4*a(n-2). - Harvey P. Dale, Oct 16 2012

Extensions

Further comments added by Antti Karttunen, Sep 14 2006