A151385 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, 0), (0, 1), (1, -1)}.

1, 1, 1, 2, 6, 12, 25, 77, 215, 511, 1466, 4610, 12680, 35579, 113158, 344542, 997244, 3112862, 9956308, 30277199, 93800266, 303919846, 963863561, 3017836845, 9766363338, 31766793517, 101462348434, 328277090248, 1079653283803, 3516292489624, 11439613075930, 37768544363774, 124746380740174

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, 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: A099495 A232164 A214663 * A034875 A136515 A141347

Adjacent sequences: A151382 A151383 A151384 * A151386 A151387 A151388

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved