A242328 a(n) = 5^n + 2.

3, 7, 27, 127, 627, 3127, 15627, 78127, 390627, 1953127, 9765627, 48828127, 244140627, 1220703127, 6103515627, 30517578127, 152587890627, 762939453127, 3814697265627, 19073486328127, 95367431640627, 476837158203127, 2384185791015627, 11920928955078127

Offset: 0

Author

Vincenzo Librandi, May 13 2014

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (6,-5).

Crossrefs

Cf. A000351, A003463, A034474, A132079, A178676, A242329.

Programs

Magma

[5^n+2: n in [0..30]];

Mathematica

Table[5^n + 2, {n, 0, 30}] (* or *) CoefficientList[Series[(3 - 11 x)/((1 - x) (1 - 5 x)), {x, 0, 30}], x]
LinearRecurrence[{6,-5},{3,7},30] (* Harvey P. Dale, Jun 30 2022 *)

Formula

G.f.: (3-11*x)/((1-x)*(1-5*x)).

a(n) = 6*a(n-1) - 5*a(n-2) for n > 1.

From Elmo R. Oliveira, Dec 04 2023: (Start)

a(n) = A000351(n) + 2.

a(n) = 5*a(n-1) - 8 with a(0) = 3.

E.g.f.: exp(5*x) + 2*exp(x). (End)