A151384 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, 2, 2, 8, 22, 56, 192, 558, 1746, 5850, 18108, 61450, 202310, 672880, 2302762, 7740494, 26610514, 91536712, 315135590, 1097812420, 3815592588, 13349580584, 46872331154, 164755197130, 582028252912, 2058703367868, 7302057111804, 25970243832668, 92497076203672, 330283889496320, 1181287444107564

Offset

0,3

Links

Table of n, a(n) for n=0..31.

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[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: A151377 A151407 A130102 * A300460 A290613 A113464

Adjacent sequences: A151381 A151382 A151383 * A151385 A151386 A151387

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved