A151397 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), (0, 1), (1, -1), (1, 0)}.

1, 1, 1, 3, 8, 15, 40, 130, 326, 854, 2812, 8328, 22849, 72679, 233635, 686180, 2131348, 7032223, 21948203, 68247127, 224907904, 731136007, 2315461477, 7582271275, 25158427804, 81559484413, 266864101260, 891674092876, 2948579481971, 9706598328841, 32479860131793, 108816989575044, 361744537905184

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, j, -1 + n] + aux[-1 + i, 1 + j, -1 + n] + aux[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: A032159 A174982 A032064 * A369711 A369983 A216466

Adjacent sequences: A151394 A151395 A151396 * A151398 A151399 A151400

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved