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A151268
Number of walks within N^2 (the first quadrant of Z^2) starting at (0,0) and consisting of n steps taken from {(-1, 1), (-1, 0), (0, -1), (0, 1), (1, -1)}
0
1, 1, 3, 7, 23, 69, 241, 815, 2973, 10765, 40599, 153519, 594441, 2315819, 9159005, 36470431, 146745519, 594261517, 2425275509, 9954790549, 41110526691, 170626390065, 711716332495, 2981638200405, 12543716384153, 52971343747061, 224502013317731, 954637799193723, 4072108059395579
OFFSET
0,3
COMMENTS
Apparently a duplicate of A148700. [From R. J. Mathar, Dec 13 2008]
LINKS
M. Bousquet-Mélou and M. Mishna, 2008. Walks with small steps in the quarter plane, ArXiv 0810.4387.
A. Bostan and M. Kauers, 2008. Automatic Classification of Restricted Lattice Walks, ArXiv 0811.2899.
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, -1 + j, -1 + n] + aux[1 + i, j, -1 + n]]; Table[Sum[aux[i, j, n], {i, 0, n}, {j, 0, n}], {n, 0, 25}]
CROSSREFS
Sequence in context: A148699 A181999 A148700 * A148701 A331685 A029891
KEYWORD
nonn,walk
AUTHOR
Manuel Kauers, Nov 18 2008
STATUS
approved