A059716 Number of column convex polyominoes with n hexagonal cells.

1, 3, 11, 42, 162, 626, 2419, 9346, 36106, 139483, 538841, 2081612, 8041537, 31065506, 120010109, 463614741, 1791004361, 6918884013, 26728553546, 103255896932, 398891029862, 1540968200661, 5952961630324, 22997069087436

Offset

1,2

Links

Michael De Vlieger, Table of n, a(n) for n = 1..1704

Moa Apagodu, Counting hexagonal lattice animals, arXiv:math/0202295 [math.CO], 2002-2009.

M. Bousquet-Mélou and A. Rechnitzer, Lattice animals and heaps of dimers

D. A. Klarner, Cell growth problems, Canad. J. Math. 19 (1967) 851-863.

K. A. Van'kov, V. M. Zhuravlyov, Regular tilings and generating functions, Mat. Pros. Ser. 3, issue 22, 2018 (127-157) [in Russian]. See page 128. - N. J. A. Sloane, Jan 09 2019

Kirill Vankov, Valerii Zhuravlev, Regular and semiregular (uniform) tilings and generating functions, hal-02535947, [math.CO], 2020.

V. M. Zhuravlev, Horizontally-convex polyiamonds and their generating functions, Mat. Pros. 17 (2013), 107-129 (in Russian).

Index entries for linear recurrences with constant coefficients, signature (6, -10, 7, -1).

Formula

G.f.: x(1-x)^3/(1-6x+10x^2-7x^3+x^4).

Maple

gf := x*(1-x)^3/(1-6*x+10*x^2-7*x^3+x^4): s := series(gf, x, 50): for i from 1 to 100 do printf(`%d, `, coeff(s, x, i)) od:

Mathematica

a[1]=1; a[2]=3; a[3]=11; a[4]=42; a[n_] := a[n] = 6*a[n-1] - 10*a[n-2] + 7*a[n-3] - a[n-4]; Table[a[n], {n, 1, 24}] (* Jean-François Alcover, Mar 30 2015 *)
LinearRecurrence[{6, -10, 7, -1}, {1, 3, 11, 42}, 24] (* Ray Chandler, Jul 16 2015 *)

Crossrefs

Sequence in context: A319512 A279704 A301483 * A122368 A344191 A032443

Adjacent sequences: A059713 A059714 A059715 * A059717 A059718 A059719

Keyword

nonn

Author

Mireille Bousquet-Mélou, Feb 08 2001

Extensions

More terms from James A. Sellers, Feb 09 2001

Status

approved