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

1,1

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. - Antti Karttunen, Sep 14 2006

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..170

Andrei Asinowski, Cyril Banderier, and 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).

Formula

a(n) = A072197(n-1) - 1 = A014486(abs(A106191(n))).

a(n) = A079946(A020988(n-2)) for n>=2. [Cf. also A122229]

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

From Elmo R. Oliveira, Mar 07 2026: (Start)

a(n) = 2*A020989(n-1).

G.f.: 2*x*(x+1)/((x-1)*(4*x-1)).

E.g.f.: (3 - 8*exp(x) + 5*exp(4*x))/6. (End)

Mathematica

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

Prog

(Magma) [(5*4^n-8)/6: n in [1..40]]; // Vincenzo Librandi, Apr 28 2011
(PARI) a(n)=(5*4^n-8)/6 \\ Charles R Greathouse IV, Oct 07 2015

Crossrefs

Cf. A014486, A020988, A072197, A079946, A106191, A122229.

Cf. A020989.

Sequence in context: A179259 A261474 A350653 * A218782 A007225 A375634

Adjacent sequences: A080672 A080673 A080674 * A080676 A080677 A080678

Keyword

nonn,easy

Author

N. J. A. Sloane, Mar 02 2003

Status

approved