OFFSET
0,4
FORMULA
a(n) = Sum_{k>=0} k * A134423(n,k).
G.f.: z^2*(1+z^2)*g^2/((1+z-z^2)*(1-3*z-z^2)), where g=1+z*g+z^2*g+z^2*g^2 (g is the g.f. of A128720).
Conjecture D-finite with recurrence -(n+2)*(5*n-7)*a(n) -(n+1)*(5*n-127)*a(n-1) +(135*n^2-655*n-42)*a(n-2) +2*(5*n^2-275*n-108)*a(n-3) +(-725*n^2+4941*n-5734)*a(n-4) +(-235*n^2+1880*n-1173)*a(n-5) +(725*n^2-6659*n+12606)*a(n-6) +2*(5*n^2+195*n-1988)*a(n-7) +(-135*n^2+1505*n-3358)*a(n-8) -(5*n+87)*(n-9)*a(n-9) +(5*n-33)*(n-10)*a(n-10)=0. - R. J. Mathar, Jul 24 2022
EXAMPLE
a(3)=4 because the areas under the paths hhh, hH, Hh, hUD, UhD and UDh are 0,0,0,1,2 and 1, respectively.
MAPLE
g:=((1-z-z^2-sqrt((1+z-z^2)*(1-3*z-z^2)))*1/2)/z^2: G:=z^2*(1+z^2)*g^2/((1+z-z^2)*(1-3*z-z^2)): Gser:=series(G, z=0, 32): seq(coeff(Gser, z, n), n=0..25);
CROSSREFS
KEYWORD
nonn
AUTHOR
Emeric Deutsch, Oct 25 2007
STATUS
approved