editing

approved

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

approved

editing

M. Bousquet-Melou 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>.

_Manuel Kauers (manuel(AT)kauers.de), _, Nov 18 2008

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

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

nonn,walk,new

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

1, 4, 42, 578, 9166, 158242, 2891042, 54993704, 1078134132, 21636311154, 442364872960, 9182624116200, 193028135699066, 4100926056901840, 87917821096174026, 1899625977112716534, 41325695763293346504, 904431694783758568086, 19899310516710760870766, 439903811117457581870242

0,2

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

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, j, -1 + n] + aux[-1 + i, 1 + j, -1 + n] + aux[1 + i, -1 + j, -1 + n] + aux[1 + i, j, -1 + n]]; Table[Sum[aux[0, k, 2 n], {k, 0, 2 n}], {n, 0, 25}]

nonn,walk

Manuel Kauers (manuel(AT)kauers.de), Nov 18 2008

approved