A151401 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), (-1, 1), (0, 1), (1, -1)}.

1, 1, 1, 3, 7, 15, 45, 123, 341, 1055, 3143, 9687, 30859, 97483, 315861, 1033493, 3395089, 11316469, 37893747, 127757627, 434147079, 1481301463, 5084504675, 17536498671, 60720379293, 211194514011, 737154897245, 2581907565225, 9073734424809, 31980512271541, 113042537052043, 400634089054315, 1423370290109371

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, -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: A050565 A097111 A371914 * A080567 A276969 A146448

Adjacent sequences: A151398 A151399 A151400 * A151402 A151403 A151404

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved