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%I #2 Nov 10 2007 03:00:00
%S 1,1,1,1,2,5,13,34,110,393,1449,5390,21534,90418,389265,1694769,
%T 7593330,34910142,163314286,772044618,3702870682,18017064221,
%U 88689351909,440271808570,2205020557614,11141413883818,56737939027682
%N First row of Modified Schroeder numbers for q=7 (A114294).
%C 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=3x/4.
%D C. Hanusa (2005). A Gessel-Viennot-Type Method for Cycle Systems with Applications to Aztec Pillows. PhD Thesis. University of Washington, Seattle, USA.
%e The number of paths from (0,0) to (5,5) staying between the lines y=x and y=3x/4 using steps of length (0,1), (1,0) and (1,1) is a(5)=5.
%Y See also A112833-A112844 and A114292-A114299.
%K nonn
%O 0,5
%A Christopher Hanusa (chanusa(AT)math.binghamton.edu), Nov 21 2005
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