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A114299 First row of Modified Schroeder numbers for q=9 (A114295). 8
1, 1, 1, 1, 1, 2, 5, 13, 34, 89, 288, 1029, 3794, 14113, 52624, 210428, 883881, 3805858, 16570925, 72497060, 325602364, 1498899060, 7017126473, 33185818242, 157858754637, 759960988368, 3706528583080, 18273586377144, 90805138443560, 453695642109973 (list; graph; refs; listen; history; text; internal format)
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
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
Sequence in context: A099496 A122367 A367658 * A112842 A097417 A367657
KEYWORD
nonn
AUTHOR
Christopher Hanusa (chanusa(AT)math.binghamton.edu), Nov 21 2005
STATUS
approved

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Last modified May 24 13:22 EDT 2024. Contains 372773 sequences. (Running on oeis4.)