A151383 Number of walks within N^2 (the first quadrant of Z^2) starting at (0,0), ending on the vertical axis and consisting of 2 n steps taken from {(-1, -1), (-1, 0), (-1, 1), (1, 1)}.

1, 3, 18, 135, 1134, 10206, 96228, 938223, 9382230, 95698746, 991787004, 10413763542, 110546105292, 1184422556700, 12791763612360, 139110429284415, 1522031755700070, 16742349312700770, 185047018719324300, 2054021907784499730, 22887672686741568420, 255925794588110265060

Offset: 0

Author

Manuel Kauers, Nov 18 2008

Keywords

• nonn
• walk

Comments

Apparently a duplicate of A005159. [R. J. Mathar, Dec 13 2008]

Links

• M. Bousquet-Mélou and M. Mishna, Walks with small steps in the quarter plane, arXiv:0810.4387 [math.CO], 2008-2009.

Programs

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, -1 + j, -1 + n] + aux[1 + i, j, -1 + n] + aux[1 + i, 1 + j, -1 + n]]; Table[Sum[aux[0, k, 2 n], {k, 0, 2 n}], {n, 0, 25}]