A151395 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, 0)}.

1, 1, 2, 5, 11, 32, 87, 248, 764, 2263, 7125, 22502, 71308, 232915, 756571, 2496821, 8313892, 27728911, 93585460, 316624455, 1077272837, 3687696937, 12654416060, 43655883878, 151090181445, 524542100001, 1827895867960, 6385078233779, 22370743311415, 78580314467710, 276639299185638, 976285257901368

Offset

0,3

Links

Table of n, a(n) for n=0..31.

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[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: A101837 A124483 A079571 * A056364 A205799 A296549

Adjacent sequences: A151392 A151393 A151394 * A151396 A151397 A151398

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved