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A059715 Number of multi-directed animals on the triangular lattice. 0
1, 3, 11, 44, 184, 790, 3450, 15242, 67895, 304267, 1369761, 6188002, 28031111, 127253141, 578694237, 2635356807, 12015117401, 54831125131, 250418753498, 1144434017309 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Counts certain animals that generalize directed animals. They are also equinumerous with a class of n-ominoes studied by Klarner in 1967.

LINKS

Table of n, a(n) for n=1..20.

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

M. Bousquet-Mélou and A. Rechnitzer, Lattice animals and heaps of dimers, Discrete Math. 258 (2002), no. 1-3, 235-274.

J.-P. Bultel, S. Giraudo, Combinatorial Hopf algebras from PROs, arXiv preprint arXiv:1406.6903 [math.CO], 2014.

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

FORMULA

The generating function is known in closed form. It is big and non-D-finite.

Bultel-Giraudo (2014), Prop. 3.2, give a g.f. - N. J. A. Sloane, Sep 21 2014

MATHEMATICA

terms = 12;

c[g_, t_] := c[g, t] = Sum[c[g, n, t], {n, 0, 2 terms}];

c[g_, n_, t_] := c[g, n, t] = P[g, n, t] - Sum[c[g, k, t] P[g, n-k-1, t], {k, 0, n-1}];

P[g_, n_, t_] := 1/F[g, n, t];

F[g_, n_, t_] := F[g, n, t] = If[n<=g, 1, F[g, n-1, t] - t F[g, n-g-1, t]];

Rest[CoefficientList[1-1/c[1, t] + O[t]^(terms+1), t]][[1 ;; terms]] (* Jean-François Alcover, Jul 25 2018 *)

CROSSREFS

Cf. A005773.

Sequence in context: A167011 A319322 A059714 * A026748 A113174 A132840

Adjacent sequences:  A059712 A059713 A059714 * A059716 A059717 A059718

KEYWORD

nonn,more

AUTHOR

Mireille Bousquet-Mélou, Feb 08 2001

STATUS

approved

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Last modified November 21 09:14 EST 2019. Contains 329362 sequences. (Running on oeis4.)