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A112830
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Table of number of domino tilings of generalized Aztec pillows of type (1, ..., 1, 3, 1, ..., 1)_n.
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1
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1, 1, 5, 1, 10, 25, 1, 17, 65, 113, 1, 26, 146, 346, 481, 1, 37, 292, 932, 1637, 1985, 1, 50, 533, 2248, 5013, 7218, 8065, 1, 65, 905, 4937, 13897, 24201, 30529, 32513, 1, 82, 1450, 10018, 35218, 74530, 108970, 126034, 130561, 1, 101, 2216, 19016, 82436
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OFFSET
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0,3
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COMMENTS
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The number of tilings of a generalized Aztec pillow of type (k 1's followed by a 3 followed by n-k-1 1's) is entry (n,k+1).
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LINKS
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FORMULA
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EXAMPLE
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The number of tilings of a generalized Aztec pillow of type (1,1,3,1)_n is entry (4,3) = 346.
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MAPLE
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matrix(11, 11, [seq([seq(((2^n-sum(binomial(n, j), j=0..k))^2+(binomial(n-1, k))^2)/2, n=k+1..k+11)], k=0..10)]);
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CROSSREFS
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KEYWORD
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AUTHOR
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Christopher Hanusa (chanusa(AT)math.binghamton.edu), Sep 21 2005
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STATUS
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approved
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