OFFSET
0,7
COMMENTS
a(n) = A191392(n,0).
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
FORMULA
G.f.: (2*(1-z^2))/(1-2*z+z^2+2*z^3+(1-z^2)*sqrt(1-4*z^2)).
a(n) ~ 9 * 2^(n-11/2) * (16+(-1)^n) / (sqrt(Pi) * n^(3/2)). - Vaclav Kotesovec, Mar 20 2014
D-finite with recurrence (n+1)*a(n) +3*(-n-1)*a(n-1) +(-5*n+13)*a(n-2) +(19*n-35)*a(n-3) +3*(n-11)*a(n-4) +2*(-17*n+73)*a(n-5) +(5*n-13)*a(n-6) +2*(13*n-77)*a(n-7) +4*(-n+8)*a(n-8) +8*(-n+8)*a(n-9)=0. - R. J. Mathar, Jul 26 2022
EXAMPLE
a(7)=3 because we have HHHHHHH, HUUDUDD, and UUDUDDH, where U=(1,1), D=(1,-1), and H=(1,0).
MAPLE
g := (2*(1-z^2))/(1-2*z+z^2+2*z^3+(1-z^2)*sqrt(1-4*z^2)): gser := series(g, z = 0, 42): seq(coeff(gser, z, n), n = 0 .. 38);
MATHEMATICA
CoefficientList[Series[(2*(1-x^2))/(1-2*x+x^2+2*x^3+(1-x^2)*Sqrt[1-4*x^2]), {x, 0, 20}], x] (* Vaclav Kotesovec, Mar 20 2014 *)
PROG
(Magma) m:=40; R<x>:=LaurentSeriesRing(RationalField(), m); Coefficients(R! (2*(1-x^2))/(1-2*x+x^2+2*x^3+(1-x^2)*Sqrt(1-4*x^2))); // Vincenzo Librandi, Mar 21 2014
CROSSREFS
KEYWORD
nonn
AUTHOR
Emeric Deutsch, Jun 04 2011
STATUS
approved