A151427 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), (0, -1), (0, 1), (1, 1)}.

1, 1, 4, 11, 42, 151, 595, 2362, 9659, 40156, 169190, 722425, 3111656, 13529583, 59224749, 261002367, 1156483097, 5150230075, 23036615255, 103451200949, 466235529649, 2108038304313, 9559470212027, 43466694363850, 198131522772553, 905184962363459, 4144132544245252, 19009670073473598

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, -1 + j, -1 + n] + aux[i, -1 + j, -1 + n] + aux[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: A149272 A149273 A149274 * A149275 A378830 A149276

Adjacent sequences: A151424 A151425 A151426 * A151428 A151429 A151430

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved