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A092438
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Sequence arising from enumeration of domino tilings of Aztec Pillow-like regions.
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2
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0, 2, 6, 26, 90, 302, 966, 3026, 9330, 28502, 86526, 261626, 788970, 2375102, 7141686, 21457826, 64439010, 193448102, 580606446, 1742343626, 5228079450, 15686335502, 47063200806, 141197991026, 423610750290, 1270865805302
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OFFSET
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0,2
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COMMENTS
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A092438(n) = Entry n+1 in row n of A092437.
A092438(n) = A046717(n+1)-2^(n+1)+1.
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REFERENCES
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J. Propp, Enumeration of matchings: problems and progress, pp. 255-291 in L. J. Billera et al., eds, New Perspectives in Algebraic Combinatorics, Cambridge, 1999 (see Problem 13).
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LINKS
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Table of n, a(n) for n=0..25.
J. Propp, Publications and Preprints
J. Propp, Enumeration of matchings: problems and progress, in L. J. Billera et al. (eds.), New Perspectives in Algebraic Combinatorics
Index to sequences with linear recurrences with constant coefficients, signature (5,-5,-5,6). [From R. J. Mathar, Apr 21 2010]
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FORMULA
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a(n)=(3^(n+1)+(-1)^(n+1))/2-2^(n+1)+1
a(n) = +5*a(n-1) -5*a(n-2) -5*a(n-3) +6*a(n-4) = 2*A140420(n) G..f: -2*x*(1-2*x+3*x^2) / ( (x-1)*(3*x-1)*(2*x-1)*(1+x) ). [From R. J. Mathar, Apr 21 2010]
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EXAMPLE
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a(3)=(3^4+(-1)^4)/2-2^4+1=26.
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CROSSREFS
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Cf. A092437-A092443.
Sequence in context: A050573 A223094 A213339 * A027207 A027231 A083845
Adjacent sequences: A092435 A092436 A092437 * A092439 A092440 A092441
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KEYWORD
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easy,nonn
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AUTHOR
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Christopher Hanusa (chanusa(AT)math.washington.edu), Mar 24 2004
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STATUS
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approved
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