A151382 Number of walks within N^2 (the first quadrant of Z^2) starting at (0,0), ending on the vertical axis and consisting of 2 n steps taken from {(-1, 1), (1, -1), (1, 1)}.

1, 1, 4, 19, 102, 594, 3654, 23365, 153764, 1034670, 7086718, 49245328, 346337916, 2460569420, 17633289260, 127316202543, 925281165610, 6763386801894, 49690473646932, 366744370456502, 2717904238032344, 20216838400382840, 150887222551436558, 1129595948426726358, 8480330828174112460

Offset

0,3

Links

Table of n, a(n) for n=0..24.

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, 1 + j, -1 + n] + aux[1 + i, -1 + j, -1 + n]]; Table[Sum[aux[0, k, 2 n], {k, 0, 2 n}], {n, 0, 25}]

Crossrefs

Sequence in context: A261490 A277956 A307678 * A234958 A188675 A199876

Adjacent sequences: A151379 A151380 A151381 * A151383 A151384 A151385

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved