A151386 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, 0)}.

1, 1, 2, 6, 14, 43, 130, 389, 1278, 4071, 13420, 45084, 150797, 516163, 1769654, 6110626, 21307611, 74431540, 261900949, 925239325, 3279526284, 11679240154, 41699500328, 149380445355, 536687090908, 1932623603426, 6977777808999, 25245964494315, 91528936623924, 332494957313551, 1209910661326539

Offset

0,3

Links

Table of n, a(n) for n=0..30.

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[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: A225172 A212197 A151414 * A151399 A299042 A152806

Adjacent sequences: A151383 A151384 A151385 * A151387 A151388 A151389

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved