A151479 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), (-1, 1), (0, -1), (0, 1), (1, 0), (1, 1)}.

1, 1, 5, 17, 77, 345, 1649, 8081, 40603, 207911, 1080842, 5691069, 30285103, 162630700, 880180326, 4796131934, 26290963023, 144882598329, 802180091860, 4460270007514, 24894507295247, 139425927499075, 783332991179825, 4413617609260839, 24933618943094571, 141197619861619694, 801383347755022792

Offset

0,3

Links

Table of n, a(n) for n=0..26.

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

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

Crossrefs

Sequence in context: A149742 A149743 A323794 * A330800 A293458 A009234

Adjacent sequences: A151476 A151477 A151478 * A151480 A151481 A151482

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved