A178676 a(n) = 5^n + 5.

6, 10, 30, 130, 630, 3130, 15630, 78130, 390630, 1953130, 9765630, 48828130, 244140630, 1220703130, 6103515630, 30517578130, 152587890630, 762939453130, 3814697265630, 19073486328130, 95367431640630, 476837158203130, 2384185791015630, 11920928955078130

Offset: 0

Author

Vincenzo Librandi, Dec 25 2010

Keywords

• nonn
• easy

Examples

			G.f. = 6 + 10*x + 30*x^2 + 130*x^3 + 630*x^4 + 3130*x^5 + 15630*x^6 + ... - _Michael Somos_, Jan 28 2019
		

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, A034474, A178671, A242328, A242329.

Programs

GAP

List([0..30], n -> 5^n +5); # G. C. Greubel, Jan 27 2019

Magma

[5^n+5: n in [0..35]];

Mathematica

Table[5^n + 5, {n, 0, 40}] (* Vincenzo Librandi, Sep 30 2013 *)

PARI

a(n)=5^n+5 \\ Charles R Greathouse IV, Oct 07 2015

Sage

[5^n+5 for n in range(40)] # G. C. Greubel, Jan 27 2019

Formula

a(n) = 5*(a(n-1) - 4) with a(0) = 6.

G.f.: (6-26*x)/((1-5*x)*(1-x)). - R. J. Mathar, Jan 05 2011

a(n) = 6*a(n-1) - 5*a(n-2) for n > 1. - Vincenzo Librandi, Sep 30 2013

E.g.f.: exp(5*x) + 5*exp(x). - G. C. Greubel, Jan 27 2019

a(n) = A000351(n)+5 = A034474(n)+4 = A242328(n)+3 = A242329(n)+1. - Elmo R. Oliveira, Dec 06 2023