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A151429 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), (0, -1), (1, 0), (1, 1)} 0
1, 0, 3, 2, 21, 35, 209, 547, 2585, 8547, 36796, 137022, 572823, 2267281, 9451024, 38678305, 162279625, 677816640, 2869255664, 12153326315, 51898954441, 222150734758, 956193664648, 4127336568163, 17888946954832, 77752439126691, 339049643912001, 1482310626668551, 6498203118707345 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..28.

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, 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: A323780 A248123 A018872 * A151475 A105525 A228772

Adjacent sequences:  A151426 A151427 A151428 * A151430 A151431 A151432

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved

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Last modified November 13 07:13 EST 2019. Contains 329085 sequences. (Running on oeis4.)