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A151420 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), (-1, 1), (0, 1), (1, -1)}. 0
1, 1, 1, 3, 9, 20, 60, 196, 589, 1907, 6516, 21860, 75589, 267566, 950279, 3423629, 12499661, 45919855, 170274916, 636617648, 2394733039, 9067049073, 34535991913, 132213431523, 508684283599, 1966124324293, 7630970742790, 29734868078582, 116292627615997, 456375717434690, 1796789652244346 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,4
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[1 + 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: A078841 A147387 A146267 * A196294 A196212 A146219
KEYWORD
nonn,walk
AUTHOR
Manuel Kauers, Nov 18 2008
STATUS
approved

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Last modified June 19 12:43 EDT 2024. Contains 373503 sequences. (Running on oeis4.)