A151354 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, 0)}.

1, 0, 1, 2, 4, 13, 36, 111, 343, 1134, 3721, 12590, 43387, 150947, 533077, 1901596, 6850513, 24882483, 91098331, 335794573, 1245510662, 4646388411, 17423439595, 65649699956, 248452918085, 944115597548, 3601177462757, 13784420392760, 52936226379611, 203912726542780, 787731869576241, 3051254511699711

Offset

0,4

Links

Table of n, a(n) for n=0..31.

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 28, Tag 37.

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, -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: A278281 A148239 A148240 * A148241 A148242 A148243

Adjacent sequences: A151351 A151352 A151353 * A151355 A151356 A151357

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved