A151420 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, 0), (-1, 1), (0, 1), (1, -1)}.

1, 1, 1, 3, 9, 20, 60, 196, 589, 1907, 6516, 21860, 75589, 267566, 950279, 3423629, 12499661, 45919855, 170274916, 636617648, 2394733039, 9067049073, 34535991913, 132213431523, 508684283599, 1966124324293, 7630970742790, 29734868078582, 116292627615997, 456375717434690, 1796789652244346

Offset

0,4

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, 1 + j, -1 + n] + aux[i, -1 + j, -1 + n] + aux[1 + i, -1 + j, -1 + n] + aux[1 + i, 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: A078841 A147387 A146267 * A196294 A196212 A146219

Adjacent sequences: A151417 A151418 A151419 * A151421 A151422 A151423

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved