A151381 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, 2, 4, 8, 18, 41, 97, 236, 584, 1474, 3770, 9767, 25575, 67592, 180128, 483502, 1306308, 3549830, 9697162, 26615698, 73366980, 203034787, 563901485, 1571351150, 4392057592, 12310850747, 34597448119, 97466655175, 275202241799, 778693720420, 2207705622668, 6270783269882, 17842662379410

Offset

0,4

Links

Table of n, a(n) for n=0..34.

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[1 + i, -1 + j, -1 + n]]; Table[Sum[aux[0, k, n], {k, 0, n}], {n, 0, 25}]

Crossrefs

Sequence in context: A333865 A274547 A112483 * A306200 A057151 A026699

Adjacent sequences: A151378 A151379 A151380 * A151382 A151383 A151384

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved