A151343 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, 1, 4, 29, 230, 2034, 19636, 200219, 2128690, 23402066, 264236768, 3049648298, 35848893160, 428019644312, 5179187934336, 63402498105619, 784107314998826, 9784873540094834, 123088167713040424, 1559540214271770126, 19887838197050534036, 255108227918077438572, 3289865618218314784376

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 7, Tag 17.
• 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, -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}]