A151443 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), (0, 1), (1, -1), (1, 1)}.

1, 1, 3, 6, 23, 57, 241, 667, 2966, 8784, 40295, 124964, 585435, 1877481, 8929621, 29378968, 141326855, 474458386, 2302594186, 7857845926, 38404279674, 132849003739, 653019772711, 2284925239463, 11285159305890, 39875000613009, 197732358849821, 704607036495398, 3505978390793893

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, 1 + j, -1 + n] + aux[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: A256674 A176424 A341549 * A148643 A240646 A148644

Adjacent sequences: A151440 A151441 A151442 * A151444 A151445 A151446

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved