A151482 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), (0, 1), (1, -1), (1, 0), (1, 1)}.

1, 1, 3, 8, 28, 93, 359, 1332, 5400, 21460, 89844, 373197, 1600682, 6853799, 29959582, 131136020, 582046108, 2590492619, 11642984469, 52500378935, 238444506195, 1086573825315, 4978762863254, 22885862700737, 105659026464329, 489244652473495, 2273483149291092, 10593076963481771, 49504781707787203

Offset

0,3

Links

Table of n, a(n) for n=0..28.

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, j, -1 + n] + aux[-1 + i, 1 + j, -1 + n] + aux[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: A148854 A148855 A148856 * A241585 A273162 A148857

Adjacent sequences: A151479 A151480 A151481 * A151483 A151484 A151485

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved