OFFSET
5,2
REFERENCES
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
M.-P. Delest and G. Viennot, Algebraic languages and polyominoes enumeration, Theoretical Computer Sci., 34 (1984), 169-206.
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 (12,-55,120,-125,54,-8).
FORMULA
G.f.: x^5*(1-3*x+2*x^2+x^3)/((1 - 3*x + x^2)^2*(1 - 6*x + 8*x^2)). - Markus Voege (voege(AT)blagny.inria.fr), Nov 28 2003
a(n) = 12*a(n-1) - 55*a(n-2) + 120*a(n-3) - 125*a(n-4) + 54*a(n-5) - 8*a(n-6) for n > 8. - Stefano Spezia, Jun 04 2024
MAPLE
A005770:=(1-3*z+2*z**2+z**3)/(4*z-1)/(2*z-1)/(z**2-3*z+1)**2; # conjectured by Simon Plouffe in his 1992 dissertation
MATHEMATICA
CoefficientList[Series[x^5*(1-3*x+2*x^2+x^3)/((1 - 3*x + x^2)^2*(1 - 6*x + 8*x^2)), {x, 0, 28}], x] (* Stefano Spezia, Jun 04 2024 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
Better description from Markus Voege (voege(AT)blagny.inria.fr), Nov 28 2003
More terms from Sean A. Irvine, Aug 26 2016
STATUS
approved