A130781 - OEIS

A130781

Sequence is identical to its third differences: a(n+3) = 3*a(n+2) - 3*a(n+1) + 2*a(n), with a(0)=a(1)=1, a(2)=2.

1, 1, 2, 5, 11, 22, 43, 85, 170, 341, 683, 1366, 2731, 5461, 10922, 21845, 43691, 87382, 174763, 349525, 699050, 1398101, 2796203, 5592406, 11184811, 22369621, 44739242, 89478485, 178956971, 357913942, 715827883, 1431655765, 2863311530

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,3

COMMENTS

The inverse binomial transform is 1,0,1,... repeated with period 3, essentiallyA011655.-R. J. Mathar,Aug 28 2023

LINKS

Table of n, a(n) for n=0..32.

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

FORMULA

3*a(n) = 2^(n+1) +A087204(n+1).

Also first differences ofA024494.

G.f.: (1-2x+2x^2)/(1-3x+3x^2-2x^3).

Binomial transform of [1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0,...]; i.e., ones in positions 2, 5, 8, 11,... and the rest zeros. [Corrected byGary W. Adamson,Jan 07 2008]

MATHEMATICA

a[n_]:= a[n] = 3 a[n - 1] - 3 a[n - 2] + 2 a[n - 3]; a[0] = a[1] = 1; a[2] = 2; Table[a@n, {n, 0, 33}] (* Or *)

CoefficientList[ Series[(1 - 2 x + 2 x^2)/(1 - 3 x + 3 x^2 - 2 x^3), {x, 0, 33}], x] (*Robert G. Wilson v,Sep 08 2007 *)

LinearRecurrence[{3, -3, 2}, {1, 1, 2}, 40] (*Harvey P. Dale,Sep 17 2013 *)

CROSSREFS

SeeA130750,A130752,A130755,A129339.

Essentially a duplicate ofA024493.

Sequence in context:A309950 A129715 A024493*A352045 A351970 A071015

Adjacent sequences:A130778 A130779 A130780*A130782 A130783 A130784

KEYWORD

nonn,easy

AUTHOR

Paul Curtz,Jul 14 2007, Jul 18 2007

EXTENSIONS

Edited byN. J. A. Sloane,Jul 28 2007

STATUS

approved