0,2

Gives the number of L-convex polyominoes with n cells, that is convex polyominoes where any two cells can be connected by a path internal to the polyomino, and which has at most 1 change of direction (i.e. one of the four orientation of the L). - Simone Rinaldi (rinaldi(AT)unisi.it), Feb 19 2007

Joe Keane (jgk(AT)jgk.org) observes that this sequence (beginning at 2) is "size of raises in pot-limit poker, one blind, maximum raising".

Dimensions of the graded components of the Hopf algebra of noncommutative multi-symmetric functions of level 2. For level r, the sequence would be the INVERT transform of binomial(n+r-1,n). - Jean-Yves Thibon (jyt(AT)univ-mlv.fr), Jun 26 2008

S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures}, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.

P. J. Cameron, Some sequences of integers, Discrete Math., 75 (1989), 89-102; also in "Graph Theory and Combinatorics 1988", ed. B. Bollobas, Annals of Discrete Math., 43 (1989), 89-102.

G. Castiglione, A. Frosini, E. Munarini, A. Restivo and S. Rinaldi, Combinatorial aspects of L-convex polyominoes, to appear in European Journal of Combinatorics, 2007.

J. Riordan, The distribution of crossings of chords joining pairs of 2n points on a circle, Math. Comp., 29 (1975), 215-222.

T. D. Noe, Table of n, a(n) for n=0..200

S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures}, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.

S. Plouffe, 1031 Generating Functions and Conjectures, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 418

Index entries for sequences related to poker

E. Duchi, S. Rinaldi, and G. Schaeffer, The number of Z-convex polyominoes

J.-C. Novelli and J.-Y. Thibon, Free quasi-symmetric functions and descent algebras for wreath products and noncommutative multi-symmetric functions

a(n) = n*a(1) + (n-1)*a(2) + ...3*a(n-2) + 2*a(n-1) - Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Aug 17 2002

G.f.: (1-x)^2/(1-4x+2x^2).

a(n+1)a(n+1) - a(n+2)a(n) = 2^n, n > 0. - Douglas Rogers, Jul 12 2004

A003480:=(z-1)**2/(1-4*z+2*z**2); [Conjectured by S. Plouffe in his 1992 dissertation.]

INVERT([seq(n+1, n=1..20)]); - Jean-Yves Thibon (jyt(AT)univ-mlv.fr), Jun 26 2008

(PARI) a(n)=polcoeff((1-x)^2/(1-4*x+2*x^2)+x*O(x^n), n)

(PARI) a(n)=local(x); if(n<1, n==0, x=(2+quadgen(8))^n; imag(x)+real(x)/2)

Row sums of A059576. Cf. A007052, A126764.

Equals (1/2) A007070, n>0.

Sequence in context: A027126 A027128 A099463 this_sequence A020727 A088854 A000777

Adjacent sequences: A003477 A003478 A003479 this_sequence A003481 A003482 A003483

nonn,easy,nice

njas

More terms from Larry Reeves (larryr(AT)acm.org), Mar 20 2000