A151494 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, 0), (0, -1), (0, 1), (1, -1), (1, 0), (1, 1)}

1, 1, 5, 17, 79, 364, 1811, 9272, 48993, 264819, 1459111, 8168870, 46354854, 266122198, 1543286620, 9029379641, 53243769463, 316161637203, 1889148487909, 11352026514978, 68565004825620, 416059778720095, 2535484046258784, 15511973547395972, 95244796176063627, 586766962036461554

Offset

0,3

Links

Table of n, a(n) for n=0..25.

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

Crossrefs

Sequence in context: A149746 A149747 A149748 * A307052 A053418 A151882

Adjacent sequences: A151491 A151492 A151493 * A151495 A151496 A151497

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved