A151412 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, 0)}.

1, 1, 3, 7, 21, 63, 198, 648, 2148, 7303, 25159, 87771, 309885, 1103217, 3961285, 14322270, 52098790, 190586734, 700547511, 2586505466, 9587737311, 35667671240, 133128177959, 498385063314, 1870940572326, 7041423384111, 26563151794983, 100425970551436, 380444157541490, 1443958508666422

Offset: 0

Author

Manuel Kauers, Nov 18 2008

Keywords

• nonn
• walk

Links

• M. Bousquet-Mélou and M. Mishna, 2008. Walks with small steps in the quarter plane, ArXiv 0810.4387.

Crossrefs

Row sums of A199915.

Programs

Mathematica

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[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}]