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A121302 Number of directed column-convex polyominoes having at least one 1-cell column. 0
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

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.

LINKS

Table of n, a(n) for n=1..28.

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.

FORMULA

G.f.: z(1-z)(1-3z+2z^2)/[(1-3z+z^2)(1-2z-z^2+z^3)].

EXAMPLE

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.

MAPLE

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);

PROG

(PARI) Vec(z*(1-z)*(1-3*z+2*z^2)/((1-3*z+z^2)*(1-2*z-z^2+z^3)) + O(z^40)) \\ Michel Marcus, Feb 14 2016

CROSSREFS

Cf. A121469, A121301.

Sequence in context: A274597 A203293 A111308 * A026150 A026123 A091468

Adjacent sequences:  A121299 A121300 A121301 * A121303 A121304 A121305

KEYWORD

nonn

AUTHOR

Emeric Deutsch, Aug 04 2006

STATUS

approved

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Last modified February 27 07:07 EST 2020. Contains 332300 sequences. (Running on oeis4.)