A151491 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), (-1, 1), (0, -1), (0, 1), (1, 0), (1, 1)}

1, 1, 7, 25, 139, 697, 3908, 21912, 127422, 750754, 4500751, 27294099, 167326836, 1034813515, 6449427761, 40464120538, 255370900987, 1620036342255, 10324927223732, 66076774941489, 424456427727545, 2735815605525049, 17687957031000077, 114680671773444382, 745458187827127822, 4857218209242641953

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[i, -1 + j, -1 + n] + aux[i, 1 + j, -1 + n] + aux[1 + 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: A057573 A082651 A241714 * A208425 A334651 A366941

Adjacent sequences: A151488 A151489 A151490 * A151492 A151493 A151494

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved