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 n steps taken from {(-1, -1), (0, -1), (0, 1), (1, -1), (1, 0)}.

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 n steps taken from {(-1, -1), (0, -1), (0, 1), (1, -1), (1, 0)}

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 n steps taken from {(-1, -1), (0, -1), (0, 1), (1, -1), (1, 0)}

1, 1, 2, 5, 13, 37, 111, 348, 1115, 3690, 12437, 42646, 148530, 523835, 1868356, 6729649, 24454173, 89552497, 330263689, 1225741014, 4575462854, 17169395749, 64738926261, 245187658138, 932406910922, 3559219448897, 13634163069767, 52398809327631, 201994189232865, 780899820381385, 3027006453635929

0,3

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

nonn,walk

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

approved