A151444 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, 0), (1, 1)}.

1, 1, 3, 8, 26, 88, 311, 1153, 4333, 16829, 66002, 264115, 1066884, 4363921, 18002965, 74905311, 313910581, 1323968067, 5616942579, 23952413637, 102631047883, 441627135110, 1907887954979, 8271997010078, 35984511382945, 157019757068451, 687117606836508, 3014802801069618, 13260483082517811

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, 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: A148814 A161938 A189177 * A151458 A290351 A148815

Adjacent sequences: A151441 A151442 A151443 * A151445 A151446 A151447

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved