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A151304 Number of walks within N^2 (the first quadrant of Z^2) starting at (0,0) and consisting of n steps taken from {(-1, 1), (-1, 0), (0, 1), (1, -1), (1, 1)} 0

%I #4 Dec 04 2016 13:57:00

%S 1,2,8,32,139,612,2780,12777,59474,279119,1319587,6272549,29957777,

%T 143629361,690899877,3332790064,16116297361,78099554494,379183671290,

%U 1844059563096,8981468647748,43802659925084,213883830813678,1045516504740462,5115841042217242,25055289097485312,122813356787701498

%N Number of walks within N^2 (the first quadrant of Z^2) starting at (0,0) and consisting of n steps taken from {(-1, 1), (-1, 0), (0, 1), (1, -1), (1, 1)}

%H M. Bousquet-Mélou and M. Mishna, 2008. Walks with small steps in the quarter plane, <a href="http://arxiv.org/abs/0810.4387">ArXiv 0810.4387</a>.

%H A. Bostan and M. Kauers, 2008. Automatic Classification of Restricted Lattice Walks, <a href="http://arxiv.org/abs/0811.2899">ArXiv 0811.2899</a>.

%t aux[i_Integer, j_Integer, n_Integer] := Which[Min[i, j, n] < 0 || Max[i, j] > n, 0, n == 0, KroneckerDelta[i, j, n], True, aux[i, j, n] = aux[-1 + i, -1 + j, -1 + n] + aux[-1 + i, 1 + j, -1 + n] + aux[i, -1 + j, -1 + n] + aux[1 + i, -1 + j, -1 + n] + aux[1 + i, j, -1 + n]]; Table[Sum[aux[i, j, n], {i, 0, n}, {j, 0, n}], {n, 0, 25}]

%K nonn,walk

%O 0,2

%A _Manuel Kauers_, Nov 18 2008

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Last modified March 28 20:05 EDT 2024. Contains 371254 sequences. (Running on oeis4.)