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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

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-Fran├žois Alcover, Dec 19 2015, after Alois P. Heinz *)

CROSSREFS

See also A112833-A112844 and A114292-A114298.

Sequence in context: A048575 A099496 A122367 * A112842 A097417 A006801

Adjacent sequences:  A114296 A114297 A114298 * A114300 A114301 A114302

KEYWORD

nonn

AUTHOR

Christopher Hanusa (chanusa(AT)math.binghamton.edu), Nov 21 2005

STATUS

approved

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Last modified January 18 04:47 EST 2019. Contains 319269 sequences. (Running on oeis4.)