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A151481 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, -1), (1, 0), (1, 1)}. 0
1, 1, 4, 13, 57, 236, 1106, 5136, 25112, 123604, 624229, 3181337, 16456910, 85845734, 452215297, 2398829267, 12815000375, 68850087543, 371908087035, 2018269612417, 10999942891088, 60181126016328, 330414426742222, 1819877327401550, 10053145748429452, 55684213462489305, 309204003830794592 (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[-1 + i, 1 + 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: A149478 A149479 A149480 * A283612 A039626 A149481
KEYWORD
nonn,walk
AUTHOR
Manuel Kauers, Nov 18 2008
STATUS
approved

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Last modified March 4 23:31 EST 2024. Contains 370537 sequences. (Running on oeis4.)