A151355 Number of walks within N^2 (the first quadrant of Z^2) starting and ending at (0,0) and consisting of n steps taken from {(-1, -1), (-1, 0), (-1, 1), (0, -1), (1, 1)}.

1, 0, 1, 2, 4, 14, 45, 120, 468, 1478, 5208, 18714, 67200, 244208, 914953, 3393606, 12865732, 48963934, 187738332, 724740954, 2816697570, 10990919138, 43152034764, 170075450764, 673260699676, 2675316693314, 10669114073080, 42685090123056, 171316969097872, 689506156453890, 2782631094476893

Offset

0,4

Links

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

A. Bostan, K. Raschel, B. Salvy, Non-D-finite excursions in the quarter plane, J. Comb. Theory A 121 (2014) 45-63, Table 1 Tag 20.

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

Crossrefs

Sequence in context: A226909 A121751 A327644 * A014272 A070822 A101536

Adjacent sequences: A151352 A151353 A151354 * A151356 A151357 A151358

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved