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A151425 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), (0, 1), (1, -1)}. 0
1, 1, 2, 4, 11, 28, 82, 242, 752, 2379, 7750, 25692, 86635, 296558, 1027851, 3603503, 12758718, 45585878, 164181411, 595669369, 2175535954, 7994009929, 29537993178, 109704376600, 409377743815, 1534371295481, 5774424726514, 21814125817926, 82700717070725, 314575421938613, 1200315307181211, 4593459795047725 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
LINKS
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[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: A005200 A148133 A148134 * A148135 A363454 A034768
KEYWORD
nonn,walk
AUTHOR
Manuel Kauers, Nov 18 2008
STATUS
approved

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Last modified June 18 23:53 EDT 2024. Contains 373490 sequences. (Running on oeis4.)