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Search: id:A123520
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| A123520 |
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Number of vertical dominoes in all possible tilings of a 2n X 3 grid by dominoes. |
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+0
2
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| 4, 28, 152, 744, 3436, 15284, 66224, 281424, 1178196, 4874444, 19973192, 81189688, 327817404, 1316035940, 5257118560, 20909651104, 82849544868, 327163551612, 1288036695544, 5057236343176, 19807689093644, 77408388584724
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OFFSET
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1,1
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COMMENT
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a(n)=Sum(k*A123519(n,k),k=0..n).
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FORMULA
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a(n)=Sum(2^(k+1)*k*binom(n+k,2k), k=0..n). G.f.=4z(1-z)/(1-4z+z^2)^2.
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EXAMPLE
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a(1)=4 because a 2 X 3 grid can be tiled in 3 ways with dominoes: 3 horizontal dominoes, 1 horizontal domino above two adjacent vertical dominoes and 1 horizontal domino below two adjacent vertical dominoes; these have altogether 4 vertical dominoes.
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MAPLE
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a:=n->sum(k*2^(k+1)*binomial(n+k, 2*k), k=0..n): seq(a(n), n=1..24);
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CROSSREFS
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Cf. A001835, A123519.
Sequence in context: A043013 A145544 A006302 this_sequence A012847 A128721 A053524
Adjacent sequences: A123517 A123518 A123519 this_sequence A123521 A123522 A123523
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KEYWORD
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nonn
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AUTHOR
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Emeric Deutsch (deutsch(AT)duke.poly.edu), Oct 16 2006
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