OFFSET
0,5
LINKS
Robert Israel, Table of n, a(n) for n = 0..2416
Yan Zhuang, A generalized Goulden-Jackson cluster method and lattice path enumeration, arXiv:1508.02793 [math.CO], 2015.
Yan Zhuang, "A generalized Goulden-Jackson cluster method and lattice path enumeration, Discrete Mathematics 341.2 (2018): 358-379.
FORMULA
G.f.: (1-2*x+2*x^2-sqrt(1-4*x+4*x^2-4*x^4+4*x^5))/(2*(x^2-x^3+x^4)).
(6+4*n)*a(n) + (-18-8*n)*a(n+1) + (18+8*n)*a(2+n) + 12*a(n+3) + (-54-8*n)*a(n+4) + (9*n+63)*a(n+5) + (-39-5*n)*a(n+6) + (9+n)*a(n+7) = 0. - Robert Israel, Feb 09 2018
MAPLE
f := gfun:-rectoproc({(6+4*n)*a(n)+(-18-8*n)*a(n+1)+(18+8*n)*a(2+n)+12*a(n+3)+(-54-8*n)*a(n+4)+(9*n+63)*a(n+5)+(-39-5*n)*a(n+6)+(9+n)*a(n+7), a(0) = 1, a(1) = 1, a(2) = 1, a(3) = 1, a(4) = 2, a(5) = 5, a(6) = 12}, a(n), remember):
map(f, [$0..100]); # Robert Israel, Feb 09 2018
MATHEMATICA
CoefficientList[Series[(1 - 2 x + 2 x^2 - Sqrt[1 - 4 x + 4 x^2 - 4 x^4 + 4 x^5]) / (2 (x^2 - x^3 + x^4)), {x, 0, 40}], x] (* Vincenzo Librandi, Feb 09 2018 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Feb 08 2018
STATUS
approved