A151446 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, 0), (-1, 1), (0, -1), (0, 1), (1, -1)}.

1, 1, 2, 5, 13, 39, 120, 393, 1327, 4621, 16507, 60136, 223256, 841162, 3213799, 12423749, 48544749, 191494444, 761889311, 3054986938, 12336481332, 50140341202, 205001854887, 842763707626, 3482160659347, 14455350510899, 60270145567922, 252314239272496, 1060308335923336, 4471663866791576

Offset

0,3

Links

Table of n, a(n) for n=0..29.

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[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[0, k, n], {k, 0, n}], {n, 0, 25}]

Crossrefs

Sequence in context: A149860 A006823 A319378 * A239106 A022894 A332415

Adjacent sequences: A151443 A151444 A151445 * A151447 A151448 A151449

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved