A151292 Number of walks within N^2 (the first quadrant of Z^2) starting at (0,0) and consisting of n steps taken from {(-1, -1), (-1, 1), (-1, 0), (0, 1), (1, 1)}

1, 2, 7, 23, 85, 314, 1207, 4682, 18493, 73688, 296671, 1202849, 4910689, 20158436, 83169871, 344628527, 1433631973, 5984532728, 25060514887, 105240685511, 443102517025, 1870054761632, 7909539602647, 33521289826778, 142330494633985, 605375433105734, 2578988979186127, 11003364185437517

Offset

0,2

Links

Table of n, a(n) for n=0..27.

A. Bostan, Computer Algebra for Lattice Path Combinatorics, Seminaire de Combinatoire Ph. Flajolet, March 28 2013.

A. Bostan and M. Kauers, Automatic Classification of Restricted Lattice Walks, arXiv:0811.2899 [math.CO], 2008-2009.

Alin Bostan, Andrew Elvey Price, Anthony John Guttmann, Jean-Marie Maillard, Stieltjes moment sequences for pattern-avoiding permutations, arXiv:2001.00393 [math.CO], 2020.

M. Bousquet-Mélou and M. Mishna, Walks with small steps in the quarter plane, arXiv:0810.4387 [math.CO], 2008-2009.

Xiang-Ke Chang, X.-B. Hu, H. Lei, Y.-N. Yeh, Combinatorial proofs of addition formulas, The Electronic Journal of Combinatorics, 23(1) (2016), #P1.8.

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] + aux[1 + i, 1 + j, -1 + n]]; Table[Sum[aux[i, j, n], {i, 0, n}, {j, 0, n}], {n, 0, 25}]

Crossrefs

CF. A151290 (similar for N^3).

Sequence in context: A150335 A150336 A173519 * A179533 A352173 A150337

Adjacent sequences: A151289 A151290 A151291 * A151293 A151294 A151295

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved