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Search: id:A121302
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| A121302 |
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Number of directed column-convex polyominoes having at least one 1-cell column. |
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1
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| 1, 1, 4, 10, 28, 75, 202, 540, 1440, 3828, 10153, 26875, 71021, 187421, 494013, 1300844, 3422509, 8998118, 23642479, 62088032, 162978242, 427648023, 1121766397, 2941697012, 7712415568, 20215976824, 52981414253, 138831400836
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OFFSET
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1,3
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COMMENT
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a(n)=Fibonacci(2n-1)-A121469(n,0) (obviously, since A121469(n,k) is the number of directed column-convex polyominoes of area n having k 1-cell columns). Column 1 of A121301.
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REFERENCES
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E. Barcucci, R. Pinzani and R. Sprugnoli, Directed column-convex polyominoes by recurrence relations, Lecture Notes in Computer Science, No. 668, Springer, Berlin (1993), pp. 282-298.
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FORMULA
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G.f.=z(1-z)(1-3z+2z^2)/[(1-3z+z^2)(1-2z-z^2+z^3)].
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EXAMPLE
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a(3)=4 because, with the exception of the 3-cell column, all the other four directed column-convex polyominoes of area 3 have a 1-cell column.
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MAPLE
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G:=z*(1-z)*(1-3*z+2*z^2)/(1-3*z+z^2)/(1-2*z-z^2+z^3): Gser:=series(G, z=0, 35): seq(coeff(Gser, z, n), n=1..32);
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CROSSREFS
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Cf. A121469, A121301.
Sequence in context: A133726 A026534 A111308 this_sequence A026150 A026123 A091468
Adjacent sequences: A121299 A121300 A121301 this_sequence A121303 A121304 A121305
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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), Aug 04 2006
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