A114297
First row of Modified Schroeder numbers for q=5 (A114293).
Original entry on oeis.org
1, 1, 1, 2, 5, 13, 42, 150, 553, 2202, 9233, 39726, 176932, 810798, 3786137, 18022100, 87265298, 428202617, 2127088358, 10684752474, 54181245592, 277101480826, 1428262595206, 7412626391101, 38712130945272, 203330779196084
Offset: 0
Christopher Hanusa (chanusa(AT)math.binghamton.edu), Nov 21 2005
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.
- C. Hanusa (2005). A Gessel-Viennot-Type Method for Cycle Systems with Applications to Aztec Pillows. PhD Thesis. University of Washington, Seattle, USA.
A114292
Modified Schroeder numbers for q=3.
Original entry on oeis.org
1, 1, 1, 2, 2, 1, 5, 5, 2, 1, 16, 16, 6, 2, 1, 57, 57, 21, 6, 2, 1, 224, 224, 82, 22, 6, 2, 1, 934, 934, 341, 89, 22, 6, 2, 1, 4092, 4092, 1492, 384, 90, 22, 6, 2, 1, 18581, 18581, 6770, 1729, 393, 90, 22, 6, 2, 1, 86888, 86888, 31644, 8044, 1794, 394, 90, 22, 6, 2, 1
Offset: 0
Christopher Hanusa (chanusa(AT)math.binghamton.edu), Nov 21 2005
The number of paths from (0,0) to (3,3) staying between the lines y=x and y=x/2 using steps of length (0,1), (1,0) and (1,1) is a(0,3)=5.
Triangle begins:
1;
1, 1;
2, 2, 1;
5, 5, 2, 1;
16, 16, 6, 2, 1;
57, 57, 21, 6, 2, 1;
224, 224, 82, 22, 6, 2, 1;
934, 934, 341, 89, 22, 6, 2, 1;
4092, 4092, 1492, 384, 90, 22, 6, 2, 1;
- C. Hanusa (2005). A Gessel-Viennot-Type Method for Cycle Systems with Applications to Aztec Pillows. PhD Thesis. University of Washington, Seattle, USA.
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b:= proc(x, y, k) option remember;
`if`(y>x or y b(n, n, k):
seq(seq(a(n,k), k=0..n), n=0..12); # Alois P. Heinz, Apr 26 2013
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b[x_, y_, k_] := b[x, y, k] = If[y>x || yJean-François Alcover, Mar 06 2015, after Alois P. Heinz *)
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