A105723 - OEIS

A105723

a(n) = 3^n - (-1)^n.

0, 4, 8, 28, 80, 244, 728, 2188, 6560, 19684, 59048, 177148, 531440, 1594324, 4782968, 14348908, 43046720, 129140164, 387420488, 1162261468, 3486784400, 10460353204, 31381059608, 94143178828, 282429536480, 847288609444, 2541865828328, 7625597484988

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OFFSET

0,2

LINKS

Muniru A Asiru, Table of n, a(n) for n = 0..2000

Dhroova Aiylam, Tanya Khovanova, Weighted Mediants and Fractals, arXiv:1711.01475 [math.NT], 2017. See p. 17.

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

FORMULA

a(n) = A102345(n) - 2*(-1)^n; (a(n) + A102345(n))/2 = A000244(n);

A007814(a(n)) = A085058(n-1) for n > 0.

E.g.f.: exp(3*x) - exp(-x). - G. C. Greubel, Nov 21 2018

G.f.: 4*x/((1+x)*(1-3*x)). - R. J. Mathar, Mar 08 2021

a(n) = 4*A015518(n). - R. J. Mathar, Mar 08 2021

MATHEMATICA

LinearRecurrence[{2, 3}, {0, 4}, 30] (* Jean-François Alcover, Nov 11 2018 *)

Table[3^n - (-1)^n, {n, 0, 30}] (* Vincenzo Librandi, Nov 21 2018 *)

PROG

(PARI) a(n) = 3^n - (-1)^n; \\ Michel Marcus, Aug 18 2017

(GAP) List([0..25], n->3^n-(-1)^n); # Muniru A Asiru, Nov 11 2018

(Magma) [3^n-(-1)^n: n in [0..30]]; // Vincenzo Librandi, Nov 21 2018

(Sage) [3^n - (-1)^n for n in range(30)] # G. C. Greubel, Nov 21 2018

CROSSREFS

Cf. A000244, A102345.

Cf. A007814, A085058.

Sequence in context: A034515 A189546 A059480 * A280118 A143555 A025234

Adjacent sequences: A105720 A105721 A105722 * A105724 A105725 A105726

KEYWORD

nonn,easy

AUTHOR

Reinhard Zumkeller, Apr 18 2005

EXTENSIONS

Corrected by T. D. Noe, Dec 11 2006

STATUS

approved