A151372 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, -1), (-1, 0), (0, -1), (0, 1), (1, 0), (1, 1)}.

1, 0, 3, 4, 26, 80, 387, 1596, 7518, 34656, 167310, 813384, 4040212, 20285408, 103195235, 530042604, 2748206006, 14362312640, 75609109594, 400620871608, 2135307326508, 11442213676512, 61615122713550, 333282537518040, 1810222600024044, 9869776566646080, 54002852920884540, 296449512451881360

Offset

0,3

Links

Table of n, a(n) for n=0..27.

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

Crossrefs

Sequence in context: A055348 A004206 A302397 * A258103 A300373 A222112

Adjacent sequences: A151369 A151370 A151371 * A151373 A151374 A151375

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved