A151317 - OEIS

A151317

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, 1), (0, 1), (1, 0), (1, 1)}.

1, 3, 12, 51, 227, 1029, 4758, 22208, 104646, 496191, 2365664, 11326328, 54426543, 262319780, 1267609850, 6139159720, 29791023708, 144814066045, 705022920195, 3437094377348, 16777086405024, 81983625331303, 401032416607965, 1963520081032578, 9621913352806611, 47187655704890669, 231584946627594022

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OFFSET

0,2

LINKS

Table of n, a(n) for n=0..26.

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[-1 + i, j, -1 + n] + aux[i, -1 + j, -1 + n] + aux[1 + i, -1 + j, -1 + n] + aux[1 + i, 1 + j, -1 + n]]; Table[Sum[aux[i, j, n], {i, 0, n}, {j, 0, n}], {n, 0, 25}]

CROSSREFS

Sequence in context: A151183 A180898 A110167 * A151184 A256334 A377582

Adjacent sequences: A151314 A151315 A151316 * A151318 A151319 A151320

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved