A151344 Number of walks within N^2 (the first quadrant of Z^2) starting and ending at (0,0) and consisting of 2 n steps taken from {(-1, -1), (-1, 0), (-1, 1), (1, -1), (1, 0)}.

1, 1, 5, 35, 313, 3253, 37540, 467990, 6190709, 85835624, 1236484572, 18384929389, 280749914660, 4386014526625, 69882361534195, 1132723613672240, 18640032332057095, 310881221313870479, 5247411904749163561, 89530524469245596005, 1542486243771208605759, 26810622290131017450845

Offset: 0

Author

Manuel Kauers, Nov 18 2008

Keywords

• nonn
• walk

Links

• 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 29, Tag 34.
• M. Bousquet-Mélou and M. Mishna, 2008. Walks with small steps in the quarter plane, ArXiv 0810.4387.

Programs

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, j, -1 + n] + aux[-1 + 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[aux[0, 0, 2 n], {n, 0, 25}]