A151394 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), (0, 1), (1, -1)}.

1, 1, 2, 3, 8, 15, 44, 91, 286, 633, 2072, 4796, 16180, 38727, 133548, 327895, 1150226, 2881857, 10247072, 26099008, 93830568, 242264113, 878987980, 2295723288, 8393889812, 22139557300, 81484257064, 216757035756, 802324361696, 2150196732767, 7998562017700, 21576806128743, 80615634684738

Offset

0,3

Comments

Apparently a duplicate of A148005. [From R. J. Mathar, Dec 13 2008]

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

Crossrefs

Sequence in context: A321231 A156802 A148005 * A148006 A148007 A148008

Adjacent sequences: A151391 A151392 A151393 * A151395 A151396 A151397

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved