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Search: id:A128102
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| A128102 |
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Number of 2 X 2 tiles in all tilings of a 4 X n rectangle with 1 X 1 and 2 X 2 square tiles. |
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+0
2
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| 0, 0, 5, 14, 69, 224, 805, 2610, 8545, 27068, 85209, 264406, 814509, 2488536, 7558093, 22827130, 68625657, 205455348, 612884929, 1822355742, 5402974789, 15977195792, 47135117493, 138757706946, 407679684497, 1195641350700
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OFFSET
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0,3
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COMMENT
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a(n)=Sum(k*A128101(n,k), k=0..2*floor(n/2)).
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REFERENCES
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S. Heubach, Tiling an m X n area with squares of size up to k X k (m <=5), Congressus Numerantium 140 (1999), pp. 43-64.
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FORMULA
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G.f.=z^2*(5-6z+3z^2)/(1-2z-3z^2+2z^3)^2.
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MAPLE
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g:=z^2*(5-6*z+3*z^2)/(1-2*z-3*z^2+2*z^3)^2: gser:=series(g, z=0, 32): seq(coeff(gser, z, n), n=0..29);
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CROSSREFS
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Cf. A128101.
Sequence in context: A165517 A004030 A166795 this_sequence A007838 A024167 A077262
Adjacent sequences: A128099 A128100 A128101 this_sequence A128103 A128104 A128105
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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), Feb 19 2007
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