OFFSET
0,4
LINKS
Ran Pan, Jeffrey B. Remmel, Paired patterns in lattice paths, arXiv:1601.07988 [math.CO], 2016.
FORMULA
a(n) = binomial(2*n,n) - A268213(n).
G.f.: (8*x^2*g(x)-(f(x)-1)*(g(x)+1)+2*x*(-2+f(x)-3*g(x)+2*f(x)*g(x))) / (16*x^2*(4*x-1)), where f(x) = sqrt(1-4*x) and g(x) = sqrt(1+4*x).
PROG
(PARI) x='x+O('x^50); f=sqrt(1-4*x); g=sqrt(1+4*x); concat([0, 0], Vec((8*x^2*g-(f-1)*(g+1)-2*x*(2-f+3*g-2*f*g))/(16*x^4*(4*x-1)))) \\ Charles R Greathouse IV, Feb 01 2016
CROSSREFS
KEYWORD
nonn
AUTHOR
Ran Pan, Jan 28 2016
STATUS
approved