A151456 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, 0), (0, -1), (1, -1), (1, 0), (1, 1)}.

1, 0, 2, 2, 10, 21, 81, 224, 803, 2561, 9050, 30870, 110319, 390692, 1416287, 5140142, 18897316, 69766341, 259721708, 971424259, 3655211118, 13814548450, 52455943266, 199966174108, 765230937806, 2938440326656, 11320368884041, 43742501535980, 169501362940771, 658540291021676, 2564869428603860

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

Crossrefs

Sequence in context: A291856 A358996 A192309 * A336490 A230893 A151389

Adjacent sequences: A151453 A151454 A151455 * A151457 A151458 A151459

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved