A151477 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), (0, 1), (1, -1), (1, 0)}.

1, 1, 3, 10, 35, 138, 566, 2431, 10780, 49067, 228355, 1081997, 5207905, 25403962, 125377203, 625176432, 3145870880, 15959346050, 81557403529, 419547453308, 2171222736256, 11298086327362, 59085844684247, 310430932981503, 1637929078223208, 8676341846872322, 46128302460092674, 246081020287578117

Offset

0,3

Links

Table of n, a(n) for n=0..27.

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[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: A149038 A097148 A149039 * A184175 A243563 A129483

Adjacent sequences: A151474 A151475 A151476 * A151478 A151479 A151480

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved