%I A114297
%S A114297 1,1,1,2,5,13,42,150,553,2202,9233,39726,176932,810798,3786137,18022100,
%T A114297 87265298,428202617,2127088358,10684752474,54181245592,277101480826,
%U A114297 1428262595206,7412626391101,38712130945272,203330779196084
%N A114297 First row of Modified Schroeder numbers for q=5 (A114293).
%C A114297 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=2x/3.
%D A114297 C. Hanusa (2005). A Gessel-Viennot-Type Method for Cycle Systems with 
               Applications to Aztec Pillows. PhD Thesis. University of Washington, 
               Seattle, USA.
%e A114297 The number of paths from (0,0) to (4,4) staying between the lines y=x 
               and y=2x/3 using steps of length (0,1), (1,0) and (1,1) is a(4)=5.
%Y A114297 See also A112833-A112844 and A114292-A114299.
%Y A114297 Sequence in context: A149872 A149873 A149874 this_sequence A119533 A066740 
               A000719
%Y A114297 Adjacent sequences: A114294 A114295 A114296 this_sequence A114298 A114299 
               A114300
%K A114297 nonn
%O A114297 0,4
%A A114297 Christopher Hanusa (chanusa(AT)math.binghamton.edu), Nov 21 2005