A151507 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, 0), (-1, 1), (0, -1), (1, -1), (1, 0)}

1, 0, 2, 1, 10, 13, 75, 158, 723, 1992, 8231, 26441, 104937, 368883, 1448498, 5379569, 21188290, 81521594, 323904187, 1276726089, 5126640363, 20567467713, 83469876148, 339473601310, 1391458427505, 5722002197888, 23665988129544, 98226229014022, 409549930220218, 1713433663235102, 7195685911351587

Offset

0,3

Links

Table of n, a(n) for n=0..30.

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, 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[0, k, n], {k, 0, n}], {n, 0, 25}]

Crossrefs

Sequence in context: A167883 A290596 A151504 * A151363 A213303 A213304

Adjacent sequences: A151504 A151505 A151506 * A151508 A151509 A151510

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved