A151408 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), (0, 1), (1, -1), (1, 0)}.

1, 1, 2, 5, 12, 34, 97, 287, 887, 2761, 8833, 28635, 93897, 312257, 1046368, 3539825, 12066283, 41387197, 142887038, 495828190, 1729130445, 6057385620, 21303526484, 75209346309, 266413953357, 946691896721, 3373935569795, 12056675023892, 43193395482458, 155104308523072, 558187652361721, 2012940278579932

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, j, -1 + n] + aux[-1 + i, 1 + j, -1 + n] + aux[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: A209798 A196545 A032292 * A121956 A348102 A176638

Adjacent sequences: A151405 A151406 A151407 * A151409 A151410 A151411

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved