OFFSET
0,1
COMMENTS
Related to Bernoulli numbers.
REFERENCES
J. Riordan, Combinatorial Identities, Wiley, 1968, p. 141.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
T. D. Noe, Table of n, a(n) for n = 0..200
Tanya Khovanova, Recursive Sequences
Simon Plouffe, Approximations de séries génératrices et quelques conjectures, Dissertation, Université du Québec à Montréal, 1992; arXiv:0911.4975 [math.NT], 2009.
Simon Plouffe, 1031 Generating Functions, Appendix to Thesis, Montreal, 1992
Index entries for linear recurrences with constant coefficients, signature (11, 1).
FORMULA
G.f.: (3 - 4*x) / (1 - 11*x - x^2). - Corrected by Colin Barker, Apr 22 2017
a(n) = Lucas(5*n+2). - Thomas Baruchel, Nov 26 2003
From Colin Barker, Apr 22 2017: (Start)
a(n) = (((11-5*sqrt(5))/2)^n*(-5+3*sqrt(5)) + (5+3*sqrt(5))*((11+5*sqrt(5))/2)^n) / (2*sqrt(5)).
a(n) = 11*a(n-1) + a(n-2) for n>1.
(End)
MAPLE
A001947:=(-3+4*z)/(-1+11*z+z**2); # Conjectured by Simon Plouffe in his 1992 dissertation.
MATHEMATICA
LucasL[5*Range[0, 20]+2] (* Harvey P. Dale, Jan 18 2012 *)
PROG
(Magma) [ Lucas(5*n +2): n in [0..120]]; // Vincenzo Librandi, Apr 16 2011
(PARI) Vec((3 - 4*x) / (1 - 11*x - x^2) + O(x^20)) \\ Colin Barker, Apr 22 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved