OFFSET
0,3
COMMENTS
Column 0 of A109191.
FORMULA
G.f.: 1/(z^2 + sqrt(1 - 2*z - 3*z^2)).
D-finite with recurrence -9*(2 + n)*(3 + n)*a(n) + (-198 - 111*n - 15*n^2)*a(n+1) + (-78 - 102*n - 24*n^2)*a(n+2) + (-462 - 340*n - 56*n^2)*a(n+3) + (-186 - 106*n - 14*n^2)*a(n+4) + (1086 + 426*n + 42*n^2)*a(n+5) + (108 + 49*n + 5*n^2)*a(n+6) + (-432 - 139*n - 11*n^2)*a(n+7) + 2*(6 + n)*(8 + n)*a(n+8) = 0. - Benedict W. J. Irwin, Nov 02 2016
EXAMPLE
a(3)=5 because we have hhh,hdu,duh,uhd and dhu.
MAPLE
g:=1/(z^2+sqrt(1-2*z-3*z^2)): gser:=series(g, z=0, 33): 1, seq(coeff(gser, z^n), n=1..31);
MATHEMATICA
CoefficientList[Series[1/(z^2+Sqrt[1-2z-3z^2]), {z, 0, 30}], z] (* Benedict W. J. Irwin, Nov 02 2016 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Emeric Deutsch, Jun 21 2005
STATUS
approved