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A151480 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, 0, 3, 3, 30, 65, 434, 1384, 7847, 30749, 162310, 714126, 3667411, 17254387, 88023109, 431259271, 2206144905, 11092437052, 57117060880, 292296895499, 1516673564569, 7861699769116, 41103663171314, 215169677630869, 1132925333732196, 5977775212622087, 31674824100293083, 168233379153239317 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..27.

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: A139206 A100651 A124244 * A096351 A086667 A067098

Adjacent sequences:  A151477 A151478 A151479 * A151481 A151482 A151483

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved

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Last modified May 25 08:37 EDT 2020. Contains 334587 sequences. (Running on oeis4.)