A151465 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, 0), (-1, 1), (0, -1), (0, 1), (1, 1)}.

1, 1, 5, 16, 69, 288, 1294, 5863, 27428, 129525, 622671, 3017788, 14788994, 72961131, 362686254, 1812678169, 9109932551, 45985005522, 233114127299, 1185997243463, 6054487301033, 31000477950556, 159174362867546, 819349202675383, 4227486665984523, 21858721760539178, 113248919676873452

Offset

0,3

Links

Table of n, a(n) for n=0..26.

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[i, -1 + j, -1 + n] + aux[i, 1 + j, -1 + n] + aux[1 + i, -1 + j, -1 + n] + aux[1 + i, 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: A220903 A042087 A332470 * A363299 A151474 A138550

Adjacent sequences: A151462 A151463 A151464 * A151466 A151467 A151468

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved