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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A101945 a(n) = 6*2^n - n - 5. 2
1, 6, 17, 40, 87, 182, 373, 756, 1523, 3058, 6129, 12272, 24559, 49134, 98285, 196588, 393195, 786410, 1572841, 3145704, 6291431, 12582886, 25165797, 50331620, 100663267, 201326562, 402653153, 805306336, 1610612703, 3221225438 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Characteristic polynomial of M = x^3 - 4x^2 + 5x - 2.

Recursive sequence generated from a 3 X 3 matrix.

No exponentiation is needed! - Vladimir Joseph Stephan Orlovsky, Oct 10 2008

LINKS

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

FORMULA

a(0)=1, a(1)=6, a(2)=17 and for n>2, a(n) = 4*a(n-1) - 5*a(n-2) + 2*a(n-3).

a(n) = right term in M^n * [1 1 1]. M^n * [1 1 1] = [1 A033484(n) a(n)].

Row sums of triangle A135855. - Gary W. Adamson, Dec 01 2007

EXAMPLE

a(5) = 182 = 4*87 - 5*40 + 2*17 = 4*a(4) - 5*a(3) + 2*a(2).

a(5) = 182 = right term in M^5 * [1 1 1]; where M^5 * [ 1 1 1] = [1 94 182] = [1 A033484(5) a(5)].

MATHEMATICA

a[0] = 1; a[1] = 6; a[2] = 17; a[n_] := a[n] = 4a[n - 1] - 5a[n - 2] + 2a[n - 3]; Table[ a[n], {n, 0, 30}] (* Robert G. Wilson v, Jan 12 2005 *)

s=1; lst={}; Do[s+=(s-n); AppendTo[lst, Abs[s]], {n, 3, 5!}]; lst (* Vladimir Joseph Stephan Orlovsky, Oct 10 2008 *)

PROG

(PARI) a(n)=if(n==1, 1, if(n==2, 6, if(n==3, 17, 4*a(n-1)-5*a(n-2)+2*a(n-3)))) \\ (Klasen)

CROSSREFS

Cf. A033484, A101946.

Cf. A135855.

Sequence in context: A080275 A061349 A213780 * A220407 A013319 A047861

Adjacent sequences:  A101942 A101943 A101944 * A101946 A101947 A101948

KEYWORD

nonn,easy

AUTHOR

Gary W. Adamson, Dec 22 2004

EXTENSIONS

More terms from Lambert Klasen (Lambert.Klasen(AT)gmx.net), Jan 06 2005

New definition from Ralf Stephan, May 17 2007

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 June 25 04:06 EDT 2019. Contains 324345 sequences. (Running on oeis4.)