A151447 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, 0), (-1, 1), (0, -1), (0, 1), (1, 0)}.

1, 1, 4, 10, 39, 130, 514, 1943, 7872, 31706, 131650, 549751, 2331370, 9963328, 42980063, 186704975, 816434120, 3590695220, 15873104022, 70496228150, 314392868577, 1407453308237, 6322525455282, 28492055193081, 128770519635266, 583542383148631, 2650954842074021, 12070587215220593

Offset

0,3

Links

Table of n, a(n) for n=0..27.

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

Crossrefs

Sequence in context: A024689 A320806 A149202 * A302183 A149203 A038168

Adjacent sequences: A151444 A151445 A151446 * A151448 A151449 A151450

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved