A242329 a(n) = 5^n + 4.

5, 9, 29, 129, 629, 3129, 15629, 78129, 390629, 1953129, 9765629, 48828129, 244140629, 1220703129, 6103515629, 30517578129, 152587890629, 762939453129, 3814697265629, 19073486328129, 95367431640629, 476837158203129, 2384185791015629, 11920928955078129

Offset: 0

Author

Vincenzo Librandi, May 13 2014

Keywords

• nonn
• easy

Comments

Subsequence of A226810. - Bruno Berselli, May 13 2014

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, A226810, A242328, A253208 (similar sequence).

Programs

Magma

[5^n+4: n in [0..30]];

Mathematica

Table[5^n + 4, {n, 0, 30}]
LinearRecurrence[{6,-5},{5,9},30] (* Harvey P. Dale, Mar 15 2025 *)

Formula

G.f.: (5-21*x)/((1-x)*(1-5*x)).

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

From Elmo R. Oliveira, Dec 06 2023: (Start)

a(n) = A000351(n)+4 = A034474(n)+3 = A242328(n)+2.

a(n) = 5*a(n-1) - 16 with a(0) = 5.

E.g.f.: exp(5*x) + 4*exp(x). (End)