1,2

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).

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

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.

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

Cf. A006027.

Sequence in context: A150659 A150660 A150661 this_sequence A143927 A060379 A002931

Adjacent sequences: A005432 A005433 A005434 this_sequence A005436 A005437 A005438

nonn,nice

Simon Plouffe (simon.plouffe(AT)gmail.com)

Corrected by Simon Plouffe.

More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu), May 13 2006