A151438 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, 1), (0, -1), (1, 0), (1, 1)}.

1, 0, 3, 3, 25, 58, 302, 1000, 4572, 17759, 78402, 327746, 1445868, 6280646, 27957450, 124210073, 558853524, 2520567027, 11454557485, 52237087015, 239457095960, 1101503925205, 5086830804442, 23565165397859, 109513332449237, 510337183030398, 2384498982840799, 11168045680153978, 52425419487599722

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[i, 1 + j, -1 + n] + aux[1 + 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: A219909 A092864 A183894 * A355558 A363471 A303822

Adjacent sequences: A151435 A151436 A151437 * A151439 A151440 A151441

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved