OFFSET
0,4
FORMULA
a(n) = Sum_{k>=0} k*A191390(n,k).
G.f.: g(z) = 4*z*(1-z)/(1-2*z+sqrt(1-4*z^2))^2.
a(0)=0 and a(n)=2^(n-1)-C(n-1,floor(n/2)-1) for n>=1. [Joerg Arndt, Aug 07 2012, aeb]
D-finite with recurrence (n+1)*a(n) +(-3*n-1)*a(n-1) +2*(-n+3)*a(n-2) +4*(3*n-8)*a(n-3) +8*(-n+4)*a(n-4)=0. - R. J. Mathar, Jul 24 2022
EXAMPLE
a(4)=5 because in (HHHH), (HH)UD, (H)UD(H), UD(HH), UDUD, and UUDD we have a total of 1+1+2+1+0+0=5 horizontal segments (shown between parentheses).
MAPLE
g := 4*z*(1-z)/(1-2*z+sqrt(1-4*z^2))^2: gser := series(g, z = 0, 40): seq(coeff(gser, z, n), n = 0 .. 35);
CROSSREFS
KEYWORD
nonn
AUTHOR
Emeric Deutsch, Jun 03 2011
STATUS
approved