A151398 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, 1)}.

1, 1, 2, 4, 11, 26, 84, 220, 742, 2070, 7197, 20922, 74432, 223010, 805708, 2470392, 9027576, 28187178, 103920850, 329292906, 1222553336, 3921481206, 14641490905, 47450199350, 177987479208, 581924348298, 2191300828800, 7219235616842, 27274167110054, 90456438360198, 342703672881624, 1143317551856284

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[-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: A340651 A123432 A345216 * A090899 A159338 A159339

Adjacent sequences: A151395 A151396 A151397 * A151399 A151400 A151401

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved