A151404 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), (0, -1), (0, 1), (1, -1)}.

1, 1, 2, 4, 9, 23, 58, 160, 447, 1280, 3799, 11329, 34648, 107194, 335052, 1062809, 3392928, 10944072, 35576811, 116369798, 383517144, 1270497711, 4232708951, 14174190320, 47670133454, 161055621043, 546226400383, 1859448826545, 6352403850949, 21770237036258, 74841611960045, 258025290079584, 891972398224757

Offset

0,3

Links

Table of n, a(n) for n=0..32.

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

Crossrefs

Row sums of A306814.

Sequence in context: A340920 A337517 A268172 * A027071 A364485 A027133

Adjacent sequences: A151401 A151402 A151403 * A151405 A151406 A151407

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved