%I A089383
%S A089383 1,8,49,280,1569,8752,48833,272976,1529441,8589176,48342449,272640680,
%T A089383 1540495553,8718956768,49423735553,280551815456,1594568513857,
%U A089383 9073566717800,51686272315569,294711466792120,1681938025818081
%N A089383 Number of peaks at even level in all Schroeder paths (i.e. consisting 
               of steps U=(1,1), D=(1,-1), H=(2,0) and never going below the axis) 
               from (0,0) to (2n+4,0).
%C A089383 Partial sums of A026002.
%F A089383 G.f.=(1-z-q)^2/[4z^2(1-z)q], where q = sqrt(1-6z+z^2).
%e A089383 a(0)=1 because the paths HH, HUD, UDH, UHD, UDUD and U(UD)D from (0,0) 
               to (4,0) have only one peak at an even level (shown between parentheses).
%Y A089383 Cf. A006318.
%Y A089383 Sequence in context: A005059 A026719 A026774 this_sequence A028443 A001108 
               A097204
%Y A089383 Adjacent sequences: A089380 A089381 A089382 this_sequence A089384 A089385 
               A089386
%K A089383 nonn
%O A089383 0,2
%A A089383 Emeric Deutsch (deutsch(AT)duke.poly.edu), Dec 28 2003