|
| |
|
|
A005435
|
|
Number of column-convex polyominoes with perimeter 2n+2.
(Formerly M1779)
|
|
3
| |
|
|
1, 2, 7, 28, 122, 558, 2641, 12822, 63501, 319554, 1629321, 8399092, 43701735, 229211236, 1210561517, 6432491192, 34364148528, 184463064936, 994430028087, 5381653402890, 29226425965907, 159227245772460, 870004781620093
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 1,2
|
|
|
REFERENCES
| R. Brak, A. J. Guttmann and I. G. Enting, Exact solution of the row-convex perimeter generating function, J. Phys. A 23 (1990), 2319-2326.
Delest, M.-P., Generating functions for column-convex polyominoes. J. Combin. Theory Ser. A 48 (1988), no. 1, 12-31.
E. Duchi and S. Rinaldi, An object grammar for column-convex polyominoes, Annals of Combinatorics, 8 (2004), 27-36.
S. Feretic, A new way of counting the column-convex polyominoes by perimeter, Discrete Math., 180, 1998, 173-184.
S. Feretic and D. Svrtan, On the number of column-convex polyominoes with given perimeter and number of columns, Proc. 5th Conf. Formal Power Series and Algebraic Combinatorics, Florence, 1993, pp. 201-214.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
|
|
|
FORMULA
| See the g.f. in the Maple program (taken from the Brak et al. paper). It has been given previously, in a different form, in the Delest paper (p. 29). - Emeric Deutsch (deutsch(AT)duke.poly.edu), May 13 2006
|
|
|
EXAMPLE
| a(3)=7 because we have: the 2 X 2 square, the 3 X 1 and 1 X 3 rectangles and the four polyominoes obtained by removing any of the four cells of the 2 X 2 square.
|
|
|
MAPLE
| G:=((y^2 - 1)*( - 21 + 47*y^2 - 35*y^4 + 5*y^6) - 3*(y^2 - 1)^2*(1 + y^2)*sqrt(1 - 6*y^2 + y^4) - 9*sqrt(2)*(y^2 - 1)^2*sqrt((y^2 - 1)^2*(1 + y^2) - (y^2 - 1)*(1 + y^2)*sqrt(1 - 6*y^2 + y^4)) - sqrt(2)*y*(y^2 - 1)*(1 + y^2)*sqrt((y^2 - 1)^2*(1 + y^2) + (y^2 - 1)*(1 + y^2)*sqrt(1 - 6*y^2 + y^4)))/(72 - 152*y^2 + 92*y^4 - 8*y^6): Gser:=series(G, y=0, 65): seq(coeff(Gser, y^(2*n)), n=2..31); - Emeric Deutsch (deutsch(AT)duke.poly.edu), May 13 2006
|
|
|
CROSSREFS
| Cf. A006027.
Sequence in context: A150659 A150660 A150661 * A143927 A060379 A002931
Adjacent sequences: A005432 A005433 A005434 * A005436 A005437 A005438
|
|
|
KEYWORD
| nonn,nice
|
|
|
AUTHOR
| Simon Plouffe (simon.plouffe(AT)gmail.com)
|
|
|
EXTENSIONS
| Corrected by Simon Plouffe.
More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu), May 13 2006
|
| |
|
|
