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
Keywords
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).
Programs
-
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 *)
Formula
G.f.: x(1-x)^3/(1-6x+10x^2-7x^3+x^4).
Extensions
More terms from James Sellers, Feb 09 2001