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A151503 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), (0, -1), (1, -1), (1, 0)} 0
1, 0, 1, 1, 3, 6, 17, 40, 117, 314, 912, 2667, 7916, 23963, 73586, 227611, 715444, 2262450, 7223397, 23261164, 75343490, 245847919, 806839587, 2661738663, 8829581024, 29418789715, 98457806482, 330890849398, 1116135299721, 3778754481148, 12835824454442, 43738283921029, 149490351563243, 512353843888497 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,5
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, j, -1 + n] + aux[-1 + i, 1 + j, -1 + n] + aux[i, 1 + 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: A291227 A027415 A280088 * A319789 A007718 A297972
KEYWORD
nonn,walk
AUTHOR
Manuel Kauers, Nov 18 2008
STATUS
approved

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Last modified May 26 10:52 EDT 2024. Contains 372824 sequences. (Running on oeis4.)