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A114294

Modified Schroeder numbers for q=7.

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 1, 5, 5, 5, 5, 2, 1, 13, 13, 13, 13, 5, 2, 1, 34, 34, 34, 34, 13, 5, 2, 1, 110, 110, 110, 110, 42, 16, 6, 2, 1, 393, 393, 393, 393, 150, 57, 21, 6, 2, 1, 1449, 1449, 1449, 1449, 553, 210, 77, 21, 6, 2, 1, 5390, 5390, 5390, 5390, 2057, 781

(list; table; graph; refs; listen; history; text; internal format)

OFFSET

0,11

COMMENTS

a(i,j) is the number of paths from (i,i) to (j,j) 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. The Hamburger Theorem implies that we can use this table to calculate the number of domino tilings of an Aztec 7-pillow (A112839). To calculate this quantity, let P_n = the principal n X n submatrix of this array. If J_n = the back-diagonal matrix of order n, then A112839(n)=det(P_n+J_nP_n^(-1)J_n).

REFERENCES

C. Hanusa (2005). A Gessel-Viennot-Type Method for Cycle Systems with Applications to Aztec Pillows. PhD Thesis. University of Washington, Seattle, USA.

LINKS

Table of n, a(n) for n=0..71.

EXAMPLE

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(0,5)=5.

CROSSREFS

See also A112833-A112844 and A114292-A114299.

Sequence in context: A281659 A345202 A308619 * A371929 A242050 A297038

Adjacent sequences: A114291 A114292 A114293 * A114295 A114296 A114297

KEYWORD

nonn,tabl

AUTHOR

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

STATUS

approved

URL: https://oeis.org/A114294

⇱ A114294 - OEIS