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A083313 a(0)=1 and a(n) = 3^n - 2^(n-1) for n>=1. 9
1, 2, 7, 23, 73, 227, 697, 2123, 6433, 19427, 58537, 176123, 529393, 1590227, 4774777, 14332523, 43013953, 129074627, 387289417, 1161999323, 3486260113, 10459304627, 31378962457, 94138984523, 282421147873, 847271832227 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Essentially the same as A064686.

Binomial transform of A051049.

LINKS

Table of n, a(n) for n=0..25.

Index entries for linear recurrences with constant coefficients, signature (5,-6).

FORMULA

a(n) = (2*3^n-(2^n-0^n))/2.

a(0) = 1, a(n) = 3^n-2^(n-1) for n>=1.

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

E.g.f.: (2*exp(3*x)-exp(2*x)+exp(0))/2.

a(n) = A090888(n-1, 4), for n > 0. - Ross La Haye, Sep 21 2004

Let b(n)=2*(3/2)^n-1. Then A003063(n)=-b(1-n)*3^(n-1) for n>0. a(n)=A064686(n)=b(n)*2^(n-1) for n>0. - Michael Somos, Aug 06 2006

From Alex Ratushnyak, Jul 03 2012: (Start)

a(n) % 100 = 23  for n = 4*k-1, k>=1.

a(n) % 100 = 27  for n = 4*k+1, k>=1.

(End)

MAPLE

A083313 := proc(n)

    if n = 0 then

        1;

    else

        3^n-2^(n-1) ;

    end if;

end proc: # R. J. Mathar, Aug 01 2013

MATHEMATICA

CoefficientList[Series[((1 - x) + (1 - 2 x) (1 - 3 x)) / (2 (1 - 2 x) (1 - 3 x)), {x, 0, 30}], x] (* Vincenzo Librandi, Feb 01 2015 *)

LinearRecurrence[{5, -6}, {1, 2, 7}, 30] (* Harvey P. Dale, Sep 04 2017 *)

PROG

(PARI) Vec(((1-x)+(1-2*x)*(1-3*x))/(2*(1-2*x)*(1-3*x)) + O(x^30)) \\ Michel Marcus, Jan 31 2015

(MAGMA) [(2*3^n-2^n+0^n)/2: n in [0..30]]; // Vincenzo Librandi, Feb 01 2015

CROSSREFS

Cf. A083314.

Sequence in context: A192906 A217664 A064686 * A077832 A030282 A291015

Adjacent sequences:  A083310 A083311 A083312 * A083314 A083315 A083316

KEYWORD

easy,nonn

AUTHOR

Paul Barry, Apr 24 2003

EXTENSIONS

Better name by Alex Ratushnyak, Jul 02 2012

STATUS

approved

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Last modified February 25 21:58 EST 2018. Contains 299660 sequences. (Running on oeis4.)