OFFSET
0,1
COMMENTS
Denoted by beta'_n by Lehmer.
REFERENCES
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
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
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
G.f.: (2-7*x-x^2-x^3)/(1-6*x+11*x^2+6*x^3+x^4).
a(n) = -2702*a(n-6) - a(n-12).
MATHEMATICA
a[0] = 2; a[1] = 5; a[2] = 7; a[3] = -26; a[n_] := a[n] = -a[n-4] - 6*a[n-3] - 11*a[n-2] + 6*a[n-1]; Table[a[n], {n, 0, 23}] (* Jean-François Alcover, May 23 2013 *)
CoefficientList[Series[(2 - 7 x - x^2 - x^3) / (1 - 6 x + 11 x^2 + 6 x^3 + x^4), {x, 0, 40], x] (* Vincenzo Librandi, Jul 21 2013 *)
LinearRecurrence[{6, -11, -6, -1}, {2, 5, 7, -26}, 40] (* Harvey P. Dale, Jun 04 2017 *)
PROG
(PARI) {a(n)=if(n>=0, polcoeff( (2-7*x-x^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( (1-x+7*x^2+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
STATUS
approved