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

Offset: 0

Author

Reinhard Zumkeller, Apr 18 2005

Keywords

• nonn
• easy

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).

Crossrefs

Cf. A000244, A102345.

Cf. A007814, A085058.

Programs

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

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 *)

PARI

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

Sage

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

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

Extensions

Corrected by T. D. Noe, Dec 11 2006