OFFSET
0,6
COMMENTS
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.
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..500
C. Hanusa, A Gessel-Viennot-Type Method for Cycle Systems with Applications to Aztec Pillows, PhD Thesis, 2005, University of Washington, Seattle, USA.
EXAMPLE
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.
MAPLE
b:= proc(x, y) option remember; `if`(y>x or y<4*x/5, 0,
`if`(x=0, 1, b(x, y-1)+b(x-1, y)+b(x-1, y-1)))
end:
a:= n-> b(n, n):
seq(a(n), n=0..35); # Alois P. Heinz, Apr 25 2013
MATHEMATICA
b[x_, y_] := b[x, y] = If[y > x || y < 4*x/5, 0, If[x == 0, 1, b[x, y-1] + b[x-1, y] + b[x-1, y-1]]]; a[n_] := b[n, n]; Table[a[n], {n, 0, 35}] (* Jean-François Alcover, Dec 19 2015, after Alois P. Heinz *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Christopher Hanusa (chanusa(AT)math.binghamton.edu), Nov 21 2005
STATUS
approved