A151391 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), (-1, 1), (0, 1), (1, 0)}.

1, 1, 2, 6, 16, 45, 142, 452, 1429, 4706, 15830, 53092, 180380, 622747, 2155976, 7495821, 26308397, 92778770, 327973373, 1165333486, 4159080037, 14877633175, 53376247653, 192149069209, 693285668555, 2506469460691, 9083812061880, 32988452185659, 119995516195356, 437257636411965, 1596078045075818

Offset

0,3

Links

Table of n, a(n) for n=0..30.

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[i, -1 + j, -1 + n] + aux[1 + 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: A337318 A333070 A290953 * A166896 A148440 A148441

Adjacent sequences: A151388 A151389 A151390 * A151392 A151393 A151394

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved