A151376 Number of walks within N^2 (the first quadrant of Z^2) starting at (0,0), ending on the vertical axis and consisting of n steps taken from {(-1, -1), (0, 1), (1, 0)}.

1, 1, 1, 3, 6, 10, 31, 72, 143, 448, 1113, 2420, 7607, 19644, 45166, 142062, 376222, 898670, 2825125, 7615948, 18705781, 58744868, 160472382, 402623434, 1262880382, 3485281642, 8893103765, 27858544576, 77513822785, 200511910392, 627320598639, 1757135458908, 4597279553057, 14365193348236

Offset

0,4

Links

Table of n, a(n) for n=0..33.

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

Crossrefs

Sequence in context: A154134 A001465 A094276 * A066245 A356977 A068821

Adjacent sequences: A151373 A151374 A151375 * A151377 A151378 A151379

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved