

A114295


Modified Schroeder numbers for q=9.


1



1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 1, 5, 5, 5, 5, 5, 2, 1, 13, 13, 13, 13, 13, 5, 2, 1, 34, 34, 34, 34, 34, 13, 5, 2, 1, 89, 89, 89, 89, 89, 34, 13, 5, 2, 1, 288, 288, 288, 288, 288, 110, 42, 16, 6, 2, 1, 1029, 1029, 1029, 1029, 1029, 393, 150, 57, 21, 6, 2, 1
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OFFSET

0,16


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=4x/5. The Hamburger Theorem implies that we can use this table to calculate the number of domino tilings of an Aztec 9pillow (A112842). To calculate this quantity, let P_n = the principal n X n submatrix of this array. If J_n = the backdiagonal matrix of order n, then A112842(n)=det(P_n+J_nP_n^(1)J_n).


REFERENCES

C. Hanusa (2005). A GesselViennotType 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..77.


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(0,6)=5.


CROSSREFS

See also A112833A112844 and A114292A114299.
Sequence in context: A104518 A329030 A027388 * A004216 A076489 A211666
Adjacent sequences: A114292 A114293 A114294 * A114296 A114297 A114298


KEYWORD

nonn,tabl


AUTHOR

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


STATUS

approved



