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A151335
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, 0), (-1, 1), (0, 1), (1, -1)}.
2
1, 0, 0, 1, 0, 1, 5, 1, 18, 43, 47, 313, 570, 1480, 5847, 11715, 41194, 124918, 317707, 1120909, 3159179, 9581991, 31624946, 92407981, 300936377, 954921610, 2965630143, 9769316877, 30986916602, 100406899586, 329864837841, 1066298792633, 3525879988702, 11612179660287, 38300799541992, 127788972039783
OFFSET
0,7
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 12
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[1 + i, -1 + j, -1 + n] + aux[1 + i, j, -1 + n]]; Table[aux[0, 0, n], {n, 0, 25}]
CROSSREFS
Sequence in context: A386678 A326121 A008971 * A297174 A226605 A389775
KEYWORD
nonn,walk
AUTHOR
Manuel Kauers, Nov 18 2008
STATUS
approved