A151461 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), (1, -1), (1, 0), (1, 1)}.

1, 0, 2, 3, 13, 34, 133, 433, 1633, 5906, 22512, 85330, 331578, 1293050, 5109327, 20311293, 81413417, 328184670, 1330967868, 5424040902, 22208746242, 91307247176, 376832905242, 1560599220086, 6483714680572, 27016498955856, 112879534190550, 472817590407516, 1985127662637080

Offset

0,3

Links

Table of n, a(n) for n=0..28.

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[-1 + 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}]

Crossrefs

Sequence in context: A299967 A216359 A169983 * A228278 A174742 A215279

Adjacent sequences: A151458 A151459 A151460 * A151462 A151463 A151464

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved