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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
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| 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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REFERENCES
| 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
| 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
| 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
| A092440(n) = Main diagonal of A112830.
A092441(n) = First sub-diagonal of A112830.
A002522(n) = column k=1 of A112830.
A066455(n) = column k=2 of A112830.
Sequence in context: A135855 A116547 A013612 * A189745 A062967 A067292
Adjacent sequences: A112827 A112828 A112829 * A112831 A112832 A112833
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KEYWORD
| easy,nonn,tabl
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AUTHOR
| Christopher Hanusa (chanusa(AT)math.binghamton.edu), Sep 21 2005
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