A151451 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, 1, 3, 9, 29, 107, 395, 1555, 6225, 25605, 107267, 456195, 1967467, 8577059, 37771451, 167734281, 750539481, 3380693983, 15318535101, 69782167449, 319415226689, 1468451997493, 6777722838993, 31396508283259, 145922107990605, 680281115404317, 3180395227067163, 14907615499732957, 70046804631141103

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[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: A151032 A007472 A292756 * A138938 A154147 A179545

Adjacent sequences: A151448 A151449 A151450 * A151452 A151453 A151454

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved