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A034474 a(n) = 5^n + 1. 58
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
a(n) is the deficiency of 3*5^n (see A033879). - Patrick J. McNab, May 28 2017
LINKS
Amelia Carolina Sparavigna, Some Groupoids and their Representations by Means of Integer Sequences, International Journal of Sciences (2019) Vol. 8, No. 10.
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)
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 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
(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
Sequence in context: A092880 A370185 A192808 * A306041 A345870 A123872
KEYWORD
nonn,easy
AUTHOR
STATUS
approved

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Last modified March 18 22:56 EDT 2024. Contains 370952 sequences. (Running on oeis4.)