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A086224 7*2^n-1. 16
6, 13, 27, 55, 111, 223, 447, 895, 1791, 3583, 7167, 14335, 28671, 57343, 114687, 229375, 458751, 917503, 1835007, 3670015, 7340031, 14680063, 29360127, 58720255, 117440511, 234881023, 469762047, 939524095, 1879048191, 3758096383 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

a(n) = A164874(n+2,2); subsequence of A030130. - Reinhard Zumkeller, Aug 29 2009

Let A be the Hessenberg matrix of order n, defined by: A[1,j]=1, A[i,i]:=-3, A[i,i-1]=-1, and A[i,j]=0 otherwise. Then, for n>=1, a(n-1)=(-1)^n*charpoly(A,-5). - Milan Janjic, Jan 27 2010

(a(n-1))^2+a(n) = (7*2^(n-1))^2 is a perfect square. - Vincenzo Librandi, Aug 08 2010

LINKS

Table of n, a(n) for n=0..29.

Index entries for linear recurrences with constant coefficients, signature (3,-2).

FORMULA

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

G.f.: (6-5*x)/((1-x)*(1-2*x)) - Jaume Oliver Lafont, Sep 14 2009

MATHEMATICA

a=6; lst={a}; k=7; Do[a+=k; AppendTo[lst, a]; k+=k, {n, 0, 5!}]; lst (* Vladimir Joseph Stephan Orlovsky, Dec 16 2008 *)

PROG

(PARI) a(n)=7<<n-1 \\ Charles R Greathouse IV, Sep 24 2015

CROSSREFS

Other sequences with recurrence a(n+1) = 2*a(n) + 1 are

a(0) = 2 gives A153893, a(0)=3 essentially A126646.

a(0) = 4 gives A153894, a(0)=5 essentially A153893.

a(0) = 7 gives essentially A000225.

a(0) = 8 gives A052996 except initial terms, a(0) =9 essentially A153894.

a(0) = 10 gives A086225, a(0) = 11 essentially A153893.

a(0) = 13 essentially A086224.

Sequence in context: A268721 A183337 A173559 * A116913 A016071 A086652

Adjacent sequences:  A086221 A086222 A086223 * A086225 A086226 A086227

KEYWORD

nonn,easy,changed

AUTHOR

Marco Matosic, Jul 27 2003

EXTENSIONS

More terms from David Wasserman, Feb 22 2005

STATUS

approved

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Last modified June 25 00:41 EDT 2017. Contains 288708 sequences.