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A059716 Number of column convex polyominoes with n hexagonal cells. 8
1, 3, 11, 42, 162, 626, 2419, 9346, 36106, 139483, 538841, 2081612, 8041537, 31065506, 120010109, 463614741, 1791004361, 6918884013, 26728553546, 103255896932, 398891029862, 1540968200661, 5952961630324, 22997069087436 (list; graph; refs; listen; history; text; internal format)
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

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Last modified December 6 09:24 EST 2021. Contains 349563 sequences. (Running on oeis4.)