

A121302


Number of directed columnconvex polyominoes having at least one 1cell 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
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OFFSET

1,3


COMMENTS

a(n) = Fibonacci(2n1)  A121469(n,0) (obviously, since A121469(n,k) is the number of directed columnconvex polyominoes of area n having k 1cell columns). Column 1 of A121301.


LINKS

Table of n, a(n) for n=1..28.
E. Barcucci, R. Pinzani and R. Sprugnoli, Directed columnconvex polyominoes by recurrence relations, Lecture Notes in Computer Science, No. 668, Springer, Berlin (1993), pp. 282298.


FORMULA

G.f.: z(1z)(13z+2z^2)/[(13z+z^2)(12zz^2+z^3)].


EXAMPLE

a(3)=4 because, with the exception of the 3cell column, all the other four directed columnconvex polyominoes of area 3 have a 1cell column.


MAPLE

G:=z*(1z)*(13*z+2*z^2)/(13*z+z^2)/(12*zz^2+z^3): Gser:=series(G, z=0, 35): seq(coeff(Gser, z, n), n=1..32);


PROG

(PARI) Vec(z*(1z)*(13*z+2*z^2)/((13*z+z^2)*(12*zz^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



