A034474 a(n) = 5^n + 1.

2, 6, 26, 126, 626, 3126, 15626, 78126, 390626, 1953126, 9765626, 48828126, 244140626, 1220703126, 6103515626, 30517578126, 152587890626, 762939453126, 3814697265626, 19073486328126, 95367431640626, 476837158203126

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

a(n) is the deficiency of 3*5^n (see A033879). - Patrick J. McNab, May 28 2017

Examples

			G.f. = 2 + 6*x + 26*x^2 + 126*x^3 + 626*x^4 + 3126*x^5 + 15626*x^6 + ...
		

Links

• T. D. Noe, Table of n, a(n) for n = 0..200
• Amelia Carolina Sparavigna, The groupoids of Mersenne, Fermat, Cullen, Woodall and other Numbers and their representations by means of integer sequences, Politecnico di Torino, Italy (2019), [math.NT].
• Amelia Carolina Sparavigna, Some Groupoids and their Representations by Means of Integer Sequences, International Journal of Sciences (2019) Vol. 8, No. 10.
• Index entries for linear recurrences with constant coefficients, signature (6,-5).

Crossrefs

Cf. A000051, A000351, A007689, A024049, A033879, A034472, A034478, A034491, A034524, A052539, A062394, A062395, A062396, A062397, A063376, A063481, A074600-A074624, A178248, A228081, A279396.

Programs

Magma

[5^n+1: n in [0..30]]; // Vincenzo Librandi, Jan 11 2017

Mathematica

Table[5^n + 1, {n, 0, 25}]
LinearRecurrence[{6,-5},{2,6},30] (* Harvey P. Dale, Jul 29 2015 *)

PARI

a(n)=5^n+1 \\ Charles R Greathouse IV, Sep 24 2015

Sage

[lucas_number2(n,6,5) for n in range(25)] # Zerinvary Lajos, Jul 08 2008

Sage

[sigma(5,n) for n in range(25)] # Zerinvary Lajos, Jun 04 2009

Sage

[5^n+1 for n in range(30)] # Bruno Berselli, Jan 11 2017

Formula

a(n) = 5*a(n-1) - 4 with a(0) = 2.

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

From Mohammad K. Azarian, Jan 02 2009: (Start)

G.f.: 1/(1-x) + 1/(1-5*x) = (2-6*x)/((1-x)*(1-5*x)).

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

a(n) = A279396(n+5,5). - Wolfdieter Lang, Jan 10 2017

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

a(n) = A000351(n) + 1.

a(n) = 2*A034478(n). (End)