OFFSET
0,1
COMMENTS
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
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).
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
KEYWORD
nonn,easy
AUTHOR
STATUS
approved