A151499 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), (-1, 1), (0, -1), (1, 0)}.

1, 0, 1, 1, 4, 5, 20, 47, 126, 327, 1041, 2854, 8083, 24892, 76208, 222509, 686079, 2174516, 6673802, 20646366, 66232829, 210542762, 662048460, 2129820354, 6910328426, 22163635347, 71624432296, 234661293959, 765583825870, 2494320434589, 8213432381547, 27116116390705, 89225059889125, 295111869092137

Offset

0,5

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

Crossrefs

Sequence in context: A293942 A064670 A119283 * A057781 A081713 A344950

Adjacent sequences: A151496 A151497 A151498 * A151500 A151501 A151502

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved