A001947 a(n) = Lucas(5*n+2). (Formerly M3120 N1265)

3, 29, 322, 3571, 39603, 439204, 4870847, 54018521, 599074578, 6643838879, 73681302247, 817138163596, 9062201101803, 100501350283429, 1114577054219522, 12360848946698171, 137083915467899403, 1520283919093591604, 16860207025497407047, 186982561199565069121

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).

Index entries for sequences related to Bernoulli numbers.

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

Sequence in context: A155651 A268020 A278934 * A323569 A049038 A091646

Adjacent sequences: A001944 A001945 A001946 * A001948 A001949 A001950

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved