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A151418 Number of walks within N^2 (the first quadrant of Z^2) starting at (0,0), ending on the vertical axis and consisting of 2 n steps taken from {(-1, 1), (1, -1), (1, 0), (1, 1)}. 0
1, 2, 11, 78, 632, 5547, 51343, 493561, 4880756, 49335396, 507489524, 5295338330, 55912919498, 596320327868, 6414558641802, 69513860916094, 758204411559337, 8317193553286408, 91698991538371147, 1015583349964628187, 11293570968982354094, 126049685734959507338, 1411563666881071642920 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
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[-1 + i, 1 + j, -1 + n] + aux[1 + i, -1 + j, -1 + n]]; Table[Sum[aux[0, k, 2 n], {k, 0, 2 n}], {n, 0, 25}]
CROSSREFS
Sequence in context: A369542 A079266 A094569 * A154273 A253256 A163203
KEYWORD
nonn,walk
AUTHOR
Manuel Kauers, Nov 18 2008
STATUS
approved

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Last modified July 22 15:28 EDT 2024. Contains 374521 sequences. (Running on oeis4.)