login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A171499 a(n) = 6*a(n-1) - 8*a(n-2) for n > 1; a(0) = 3, a(1) = 14. 8
3, 14, 60, 248, 1008, 4064, 16320, 65408, 261888, 1048064, 4193280, 16775168, 67104768, 268427264, 1073725440, 4294934528, 17179803648, 68719345664, 274877644800, 1099511103488, 4398045462528, 17592183947264, 70368739983360 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

Binomial transform of A171498; second binomial transform of A171497; third binomial transform of A010703.

Related to sequences A001969 and A000069, sum of each group with exponent 1. - Eric Desbiaux, Jul 24 2013

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..500

Index entries for linear recurrences with constant coefficients, signature (6,-8)

FORMULA

a(n) = 4*4^n - 2^n = 2^n * (2^(n+2)-1).

G.f.: (3-4*x)/((1-2*x)*(1-4*x)).

a(n) = 4*a(n-1)+2^n, a(0)=3; a(n) = 6*a(n-1) - 8*a(n-2). [Vincenzo Librandi, Jul 18 2011]

MATHEMATICA

(* This program shows how A171499 arises from the Vandermonde determinant of (1, 2, 4, ..., 2^(n-1)). *)

f[j_] := 2^(j - 1); z = 15;

v[n_] := Product[Product[f[k] - f[j], {j, 1, k - 1}], {k, 2, n}]

d[n_] := Product[(i - 1)!, {i, 1, n}]

Table[v[n], {n, 1, z}]               (* A203303 *)

Table[v[n + 1]/v[n], {n, 1, z - 1}]  (* A002884 *)

Table[v[n] v[n + 2]/(2*v[n + 1]^2),

  {n, 1, z - 1}]                       (* A171499 *)

(* Clark Kimberling, Jan 02 2011 *)

PROG

(PARI) {m=23; v=concat([3, 14], vector(m-2)); for(n=3, m, v[n]=6*v[n-1]-8*v[n-2]); v}

(MAGMA) [4*4^n-2^n: n in [0..30]]; // Vincenzo Librandi, Jul 18 2011

CROSSREFS

Cf. A010703, A171497, A171498, A171472, A171473.

Sequence in context: A006224 A219544 A131262 * A006502 A024037 A281349

Adjacent sequences:  A171496 A171497 A171498 * A171500 A171501 A171502

KEYWORD

nonn,easy

AUTHOR

Klaus Brockhaus, Dec 10 2009

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified October 23 07:11 EDT 2019. Contains 328336 sequences. (Running on oeis4.)