1,2

a(n) = total number of weak plateaus in all Schroeder n-paths. A weak plateau is a subpath of the form UFF..FD where there are 0 or more Fs. For example, a(2)=6 counts the following weak plateaus (in parentheses) in the 6 Schroeder 2-paths: (UFD), U(UD)D, FF, (UD)F, F(UD), (UD)(UD). - David Callan (callan(AT)stat.wisc.edu), Aug 16 2006

G.f. = [1/sqrt(1-6z+z^2)-1/(1-z)]/2. - Emeric Deutsch (deutsch(AT)duke.poly.edu), Dec 25 2003

a(n) = sum( binomial(2*j-1, j-1) * binomial(n+j, 2*j), j, 1, n) - Stefan Hollos (stefan(AT)exstrom.com), Jul 21 2004

seq(add(multinomial(n+k, n-k, k, k)/2, k=1..n), n=1..22); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Oct 18 2006

a:=n->sum(sum(binomial(n, j)*binomial(n, k)*binomial(k, j), j=0..n), k=1..n): seq(a(n)/2, n=1..22); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 02 2007

2*a(n)+1 = A001850(n).

a(n)=sum(k=0..n l=0..n T(k, l)), array T as in A008288.

Sequence in context: A077352 A038223 A022034 this_sequence A003128 A058146 A015449

Adjacent sequences: A047662 A047663 A047664 this_sequence A047666 A047667 A047668

nonn

D. E. Knuth, N. J. A. Sloane (njas(AT)research.att.com).