A151365 Number of walks within N^2 (the first quadrant of Z^2) starting and ending at (0,0) and consisting of n steps taken from {(-1, -1), (-1, 0), (0, -1), (0, 1), (1, 1)}.

1, 0, 2, 2, 11, 27, 101, 348, 1237, 4752, 17552, 69635, 269504, 1085729, 4351437, 17775548, 72934213, 302080006, 1259717600, 5283979096, 22304022387, 94582158638, 403155327233, 1725391432093, 7415018474585, 31980782229030, 138409663709656, 600908838337016, 2616559379817830

Offset

0,3

Links

Table of n, a(n) for n=0..28.

A. Bostan, K. Raschel, B. Salvy, Non-D-finite excursions in the quarter plane, J. Comb. Theory A 121 (2014) 45-63, Table 1 Tag 25, Tag 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, j, -1 + n] + aux[1 + i, 1 + j, -1 + n]]; Table[aux[0, 0, n], {n, 0, 25}]

Crossrefs

Sequence in context: A235606 A175202 A187430 * A244280 A090527 A014220

Adjacent sequences: A151362 A151363 A151364 * A151366 A151367 A151368

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved