A151454 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), (0, -1), (0, 1), (1, -1), (1, 0)}.

1, 1, 3, 7, 23, 70, 244, 841, 3070, 11321, 42892, 164826, 643171, 2541709, 10150613, 40950489, 166560231, 682877583, 2818508803, 11707406237, 48902588515, 205338043520, 866285629022, 3670743481964, 15617076958146, 66691294104345, 285791267050047, 1228667049796098, 5298267508471368

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, j, -1 + n] + aux[-1 + i, 1 + j, -1 + n] + aux[i, -1 + j, -1 + n] + aux[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: A148701 A331685 A029891 * A106936 A088704 A341072

Adjacent sequences: A151451 A151452 A151453 * A151455 A151456 A151457

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved