A151402 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, 0), (-1, 1), (1, -1), (1, 1)}.

1, 2, 16, 140, 1484, 16980, 205928, 2602288, 33905132, 452379572, 6151336384, 84946062728, 1188189370528, 16800487225008, 239754113567120, 3448822932316384, 49956590631943196, 728060439341088052, 10668222493094013264, 157076944403690869624, 2322806732581652247624, 34483375160100269296920

Offset

0,2

Links

Table of n, a(n) for n=0..21.

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

Crossrefs

Sequence in context: A369580 A056662 A348618 * A365526 A199565 A003768

Adjacent sequences: A151399 A151400 A151401 * A151403 A151404 A151405

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved