A151419 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), (1, 1)}.

1, 0, 3, 4, 20, 60, 227, 808, 3146, 11798, 46638, 182794, 729704, 2930082, 11866477, 48312364, 198017220, 815038874, 3370875226, 13995160516, 58314718458, 243770271046, 1022058534364, 4296650572370, 18107826477884, 76487043063264, 323759955579550, 1373105848933180, 5834053915245474

Offset

0,3

Links

Table of n, a(n) for n=0..28.

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[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: A222763 A306668 A300499 * A067281 A326424 A151357

Adjacent sequences: A151416 A151417 A151418 * A151420 A151421 A151422

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved