A151390 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, -1)}.

1, 1, 1, 2, 6, 13, 33, 88, 256, 706, 2150, 6274, 19646, 59393, 190957, 592500, 1940660, 6150996, 20448656, 65920110, 221846298, 725218554, 2465440766, 8154637122, 27960144414, 93407091930, 322618540398, 1087075564126, 3778473023706, 12827256622881, 44832392213325, 153201067563940, 538068545212932

Offset

0,4

Links

Table of n, a(n) for n=0..32.

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, -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: A244578 A238827 A098407 * A116426 A196906 A162057

Adjacent sequences: A151387 A151388 A151389 * A151391 A151392 A151393

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved