OFFSET
0,2
COMMENTS
omega is a primitive third root of unity. - Joerg Arndt, Apr 29 2021
REFERENCES
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
H. W. Lenstra, Jr., Letter to N. J. A. Sloane, Nov. 1975
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.
P. Samuel, About Euclidean rings, J. Alg., 19 (1971), 282-301.
Index entries for linear recurrences with constant coefficients, signature (5,-5,-5,4,8,-6).
FORMULA
a(n+6) - 5*a(n+5) + 5*a(n+4) + 5*a(n+3) - 4*a(n+2) - 8*a(n+1) + 6*a(n) = 0.
G.f.: (x*(6*x^4+2*x^3+x+2)+1)/((x-1)^2*(3*x-1)*(2*x^2*(x+1)-1)). - Harvey P. Dale, Mar 03 2012
MAPLE
A006458:=(1+2*z+z**2+2*z**4+6*z**5)/(3*z-1)/(2*z**3+2*z**2-1)/(z-1)**2; # Conjectured by Simon Plouffe in his 1992 dissertation
MATHEMATICA
LinearRecurrence[{5, -5, -5, 4, 8, -6}, {1, 7, 31, 115, 391, 1267}, 40] (* Harvey P. Dale, Mar 03 2012 *)
CROSSREFS
KEYWORD
nonn,easy,nice
AUTHOR
H. W. Lenstra, Jr
EXTENSIONS
Corrected by T. D. Noe, Nov 08 2006
More terms from Harvey P. Dale, Mar 03 2012
Name corrected by Joerg Arndt, Apr 29 2021
STATUS
approved