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A151438 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, 1), (0, -1), (1, 0), (1, 1)}. 0
1, 0, 3, 3, 25, 58, 302, 1000, 4572, 17759, 78402, 327746, 1445868, 6280646, 27957450, 124210073, 558853524, 2520567027, 11454557485, 52237087015, 239457095960, 1101503925205, 5086830804442, 23565165397859, 109513332449237, 510337183030398, 2384498982840799, 11168045680153978, 52425419487599722 (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[-1 + i, j, -1 + n] + aux[i, 1 + j, -1 + n] + aux[1 + 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: A219909 A092864 A183894 * A355558 A363471 A303822
KEYWORD
nonn,walk
AUTHOR
Manuel Kauers, Nov 18 2008
STATUS
approved

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Last modified July 17 05:50 EDT 2024. Contains 374360 sequences. (Running on oeis4.)