A151414 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), (1, -1), (1, 1)}.

1, 0, 1, 2, 6, 14, 43, 126, 396, 1230, 3970, 12830, 42478, 140982, 475671, 1608542, 5508488, 18900350, 65498136, 227340182, 795468118, 2787057078, 9830186006, 34711199838, 123255087526, 438093298054, 1564557142054, 5592309891438, 20070764026326, 72089179111398, 259844964879959, 937255549483022, 3391151925316544

Offset

0,4

Links

Table of n, a(n) for n=0..32.

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]]; Table[Sum[aux[0, k, n], {k, 0, n}], {n, 0, 25}]

Crossrefs

Sequence in context: A281707 A225172 A212197 * A151386 A151399 A299042

Adjacent sequences: A151411 A151412 A151413 * A151415 A151416 A151417

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved