%I A114299
%S A114299 1,1,1,1,1,2,5,13,34,89,288,1029,3794,14113,52624,210428,883881,3805858,
%T A114299 16570925,72497060,325602364,1498899060,7017126473,33185818242,
%U A114299 157858754637,759960988368,3706528583080,18273586377144,90805138443560
%N A114299 First row of Modified Schroeder numbers for q=9 (A114295).
%C A114299 a(i) is the number of paths from (0,0) to (i,i) using steps of length 
               (0,1), (1,0) and (1,1), not passing above the line y=x nor below 
               the line y=4x/5.
%D A114299 C. Hanusa (2005). A Gessel-Viennot-Type Method for Cycle Systems with 
               Applications to Aztec Pillows. PhD Thesis. University of Washington, 
               Seattle, USA.
%e A114299 The number of paths from (0,0) to (6,6) staying between the lines y=x 
               and y=4x/5 using steps of length (0,1), (1,0) and (1,1) is a(6)=5.
%Y A114299 See also A112833-A112844 and A114292-A114298.
%Y A114299 Sequence in context: A001519 A048575 A099496 this_sequence A112842 A097417 
               A006801
%Y A114299 Adjacent sequences: A114296 A114297 A114298 this_sequence A114300 A114301 
               A114302
%K A114299 nonn
%O A114299 0,6
%A A114299 Christopher Hanusa (chanusa(AT)math.binghamton.edu), Nov 21 2005