A151475 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), (1, -1), (1, 0), (1, 1)}.

1, 0, 3, 2, 23, 35, 258, 591, 3538, 10378, 55110, 189260, 937965, 3566795, 17014249, 69167067, 323493034, 1374890250, 6373894066, 27922300363, 129121327852, 577728005802, 2674276420225, 12149013493835, 56397695554652, 259129442571387, 1207399214941454, 5596251474948357, 26180522045526490

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[-1 + i, j, -1 + n] + aux[-1 + 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: A329441 A151429 A355290 * A105525 A228772 A165714

Adjacent sequences: A151472 A151473 A151474 * A151476 A151477 A151478

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved