OFFSET
0,2
COMMENTS
Denoted by beta_n by Lehmer.
REFERENCES
B. C. Berndt, Ramanujan's Notebooks Part IV, Springer-Verlag, see p. 84.
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
Robert Israel, Table of n, a(n) for n = 0..1746
D. H. Lehmer, Lacunary recurrence formulas for the numbers of Bernoulli and Euler, Annals Math., 36 (1935), 637-649.
Index entries for linear recurrences with constant coefficients, signature (6,-11,-6,-1).
FORMULA
a(0)..a(11) are as given (with signs); for n >= 12, a(n) = -2702*a(n-6) - a(n-12).
G.f.: (2x^3 + 7x^2 - x + 1)/(x^4 + 6x^3 + 11x^2 - 6x + 1).
a(0)=1, a(1)=5, a(2)=26, a(3)=97, a(n) = 6*a(n-1) - 11*a(n-2) - 6*a(n-3) - a(n-4). - Harvey P. Dale, Jun 13 2011
MAPLE
f:= gfun:-rectoproc({a(0)=1, a(1)=5, a(2)=26, a(3)=97, a(n)=6*a(n-1)-11*a(n-2)-6*a(n-3)-a(n-4)}, a(n), remember):
map(f, [$0..25]); # Robert Israel, Aug 23 2017
MATHEMATICA
LinearRecurrence[{6, -11, -6, -1}, {1, 5, 26, 97}, 30] (* or *) CoefficientList[ Series[(2x^3+7x^2-x+1)/(x^4+6x^3+11x^2-6x+1), {x, 0, 30}], x] (* Harvey P. Dale, Jun 13 2011 *)
PROG
(PARI) {a(n)=if(n>=0, polcoeff( (1-x+7*x^2+2*x^3)/(1-6*x+11*x^2+6*x^3+x^4) +x*O(x^n), n), n=-1-n; (-1)^n*polcoeff( (2-7*x-x^2-x^3)/(1-6*x+11*x^2+6*x^3+x^4) +x*O(x^n), n) )} /* Michael Somos, Mar 27 2005 */
CROSSREFS
KEYWORD
sign,easy
AUTHOR
EXTENSIONS
More terms from James A. Sellers, Dec 23 1999
STATUS
approved