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

Offset

0,1

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).

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

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 *)

Prog

(Magma)[3^n+3: n in [0..35]];
(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
(GAP) List([0..40], n -> 3^n+3); # G. C. Greubel, Jan 27 2019

Crossrefs

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

Sequence in context: A056495 A351523 A263656 * A025018 A102043 A025017

Adjacent sequences: A178671 A178672 A178673 * A178675 A178676 A178677

Keyword

nonn,easy

Author

Vincenzo Librandi, Dec 25 2010

Status

approved