A151399 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), (1, 0), (1, 1)}.

1, 1, 2, 6, 14, 44, 132, 401, 1327, 4231, 14123, 47537, 160013, 551377, 1895851, 6587958, 23061992, 80886997, 285961506, 1013609292, 3607287249, 12892376175, 46181318719, 166012613410, 598252219576, 2160943489509, 7825226695478, 28390138542713, 103212631759477, 375912446455116, 1371356707626747

Offset

0,3

Links

Table of n, a(n) for n=0..30.

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

Crossrefs

Sequence in context: A212197 A151414 A151386 * A299042 A152806 A366223

Adjacent sequences: A151396 A151397 A151398 * A151400 A151401 A151402

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved