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 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 (list; table; graph; refs; listen; history; text; internal format)
 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 9-pillow (A112842). 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 A112842(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 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 A112833-A112844 and A114292-A114299. 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

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Last modified May 9 00:09 EDT 2021. Contains 343685 sequences. (Running on oeis4.)