A151466 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, 0, 3, 4, 30, 74, 453, 1538, 8344, 33896, 175156, 786236, 3998516, 19030790, 96707373, 477125050, 2438452956, 12316179442, 63449322110, 325748325720, 1692206506392, 8793471171194, 46041655934954, 241520822902712, 1273626835517006, 6732473578292730, 35728803159943962, 190081197310435600

Offset

0,3

Links

Table of n, a(n) for n=0..27.

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, 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: A076001 A225629 A032833 * A347978 A127068 A058603

Adjacent sequences: A151463 A151464 A151465 * A151467 A151468 A151469

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved