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Lattice animals on a staircase and generalized Fibonacci numbers

L. Turban
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Abstract

We study the statistics of column-convex lattice animals generated by the stacking of squares on a staircase with step height p. We calculate the number of animals with area k living on l stairs. The total number of animals with area k is given by the generalized Fibonacci number F_p(k). Exact results for the mean length and mean height of animals with area k are also obtained and we examine their asymptotic behaviour.

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L. Turban. 2006-10-19. Lattice animals on a staircase and generalized Fibonacci numbers. https://arxiv.org/abs/cond-mat/0106595

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