A151500 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, -1), (-1, 1), (1, -1), (1, 0)}

1, 1, 5, 28, 202, 1634, 14356, 134442, 1320582, 13475838, 141858494, 1532365936, 16917613816, 190293921824, 2175382137928, 25222807343938, 296126634648206, 3515506441807942, 42152202377678462, 509971838967101524, 6220118724701272900, 76429469578696026476, 945490543715011286048

Offset

0,3

Links

Table of n, a(n) for n=0..22.

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

Crossrefs

Sequence in context: A064898 A368792 A216586 * A356409 A332711 A292426

Adjacent sequences: A151497 A151498 A151499 * A151501 A151502 A151503

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved