A164051 a(n) = 2^(2n) + 2^(n-1).

5, 18, 68, 264, 1040, 4128, 16448, 65664, 262400, 1049088, 4195328, 16779264, 67112960, 268443648, 1073758208, 4295000064, 17179934720, 68719607808, 274878169088, 1099512152064, 4398047559680, 17592188141568, 70368748371968, 281474985099264

Offset: 1

Author

Jaroslav Krizek, Aug 08 2009

Keywords

• nonn
• easy

Comments

A bisection of A001445.

a(n) written in base 2: 101, 10010, 1000100, 100001000, ..., i.e. number 1, n times 0, number 1, (n-1) times 0 (see A164367). [Jaroslav Krizek, Aug 14 2009]

Links

• G. C. Greubel, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (6,-8).

Programs

Mathematica

Table[2^(2 n) + 2^(n - 1), {n, 24}] (* or *)
Rest@ CoefficientList[Series[-x (-5 + 12 x)/((4 x - 1) (2 x - 1)), {x, 0, 24}], x] (* Michael De Vlieger, Jun 21 2016 *)
LinearRecurrence[{6,-8},{5,18},30] (* Harvey P. Dale, Jan 07 2023 *)

PARI

x='x+O('x^50); Vec(x*(5-12*x)/((1-4*x)*(1-2*x))) \\ G. C. Greubel, Sep 08 2017

PARI

a(n) = 2^(2*n) + 2^(n-1); \\ Michel Marcus, Sep 09 2017

Formula

a(n) = A001445(2n+1).

a(n) = 6*a(n-1) - 8*a(n-2).

G.f.: x*(5-12*x)/((1-4*x)*(1-2*x)).

E.g.f.: (-3 + exp(2*x) + 2*exp(4*x))/2. - Ilya Gutkovskiy, Jun 21 2016

Extensions

Edited and extended by R. J. Mathar, Aug 11 2009