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A034474 a(n) = 5^n + 1. 51
2, 6, 26, 126, 626, 3126, 15626, 78126, 390626, 1953126, 9765626, 48828126, 244140626, 1220703126, 6103515626, 30517578126, 152587890626, 762939453126, 3814697265626, 19073486328126, 95367431640626, 476837158203126 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

Numbers n for which the expression 5^n/(n-1) is an integer. - Paolo P. Lava, May 29 2006

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

LINKS

T. D. Noe, Table of n, a(n) for n = 0..200

Index entries for linear recurrences with constant coefficients, signature (6,-5).

FORMULA

a(n) = 5*a(n-1) - 4 = 6*a(n-1) - 5*a(n-2).

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

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

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

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

EXAMPLE

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

MATHEMATICA

Table[5^n + 1, {n, 0, 25}]

LinearRecurrence[{6, -5}, {2, 6}, 30] (* Harvey P. Dale, Jul 29 2015 *)

PROG

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

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

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

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

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

CROSSREFS

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

Sequence in context: A208034 A092880 A192808 * A123872 A230071 A030937

Adjacent sequences:  A034471 A034472 A034473 * A034475 A034476 A034477

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified August 18 19:41 EDT 2017. Contains 290762 sequences.