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Search: id:A114293
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| A114293 |
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Modified Schroeder numbers for q=5. |
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+0
3
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| 1, 1, 1, 1, 1, 1, 2, 2, 2, 1, 5, 5, 5, 2, 1, 13, 13, 13, 5, 2, 1, 42, 42, 42, 16, 6, 2, 1, 150, 150, 150, 57, 21, 6, 2, 1, 553, 553, 553, 210, 77, 21, 6, 2, 1, 2202, 2202, 2202, 836, 306, 82, 22, 6, 2, 1, 9233, 9233, 9233, 3505, 1282, 341, 89, 22, 6, 2, 1, 39726, 39726, 39726
(list; table; graph; listen)
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OFFSET
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0,7
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COMMENT
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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=2x/3. The Hamburger Theorem implies that we can use this table to calculate the number of domino tilings of an Aztec 5-pillow (A112836). 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 A112836(n)=det(P_n+J_nP_n^(-1)J_n).
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REFERENCES
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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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EXAMPLE
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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(0,4)=5.
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CROSSREFS
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See also A112833-A112844 and A114292-A114299.
Sequence in context: A071458 A131308 A109978 this_sequence A086612 A128207 A037867
Adjacent sequences: A114290 A114291 A114292 this_sequence A114294 A114295 A114296
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KEYWORD
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nonn,tabl
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AUTHOR
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Christopher Hanusa (chanusa(AT)math.binghamton.edu), Nov 21 2005
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