A178674 a(n) = 3^n + 3.

4, 6, 12, 30, 84, 246, 732, 2190, 6564, 19686, 59052, 177150, 531444, 1594326, 4782972, 14348910, 43046724, 129140166, 387420492, 1162261470, 3486784404, 10460353206, 31381059612, 94143178830, 282429536484, 847288609446, 2541865828332, 7625597484990, 22876792454964

Offset: 0

Author

Vincenzo Librandi, Dec 25 2010

Keywords

• nonn
• easy

Comments

a(n) is the deficiency of 3^n * 5. - Patrick J. McNab, May 27 2017

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (4,-3).

Crossrefs

Cf. A034472, A115098, A168607, A168609, A168610.

Programs

GAP

List([0..40], n -> 3^n+3); # G. C. Greubel, Jan 27 2019

Magma

[3^n+3: n in [0..35]];

Mathematica

Table[3^n+3, {n, 0, 40}] (* or *) CoefficientList[Series[(4-10x)/((1-x) (1-3x)), {x, 0, 30}], x] (* Vincenzo Librandi, May 13 2014 *)

PARI

a(n)=3^n+3 \\ Charles R Greathouse IV, Oct 07 2015

Sage

[3^n+3 for n in range(40)] # G. C. Greubel, Jan 27 2019

Formula

a(n) = 3*(a(n-1) - 2), a(0)=4.

From R. J. Mathar, Jan 05 2011: (Start)

G.f.: (4-10*x)/((1-3*x)*(1-x)).

a(n) = 2*A115098(n). (End)

a(n) = 4*a(n-1) - 3*a(n-2) for n > 1. - Vincenzo Librandi, May 13 2014

E.g.f.: exp(x)*(exp(2*x) + 3). - Elmo R. Oliveira, Apr 02 2025