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A151282
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Number of walks within N^2 (the first quadrant of Z^2) starting at (0,0) and consisting of n steps taken from {(-1, -1), (-1, 0), (0, 1), (1, 1)}
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0
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1, 2, 6, 18, 58, 190, 638, 2170, 7474, 25974, 90982, 320738, 1137002, 4049838, 14485326, 52001290, 187292514, 676546790, 2450311862, 8895769714, 32366225562, 117995832990, 430960312862, 1576675041434, 5777325893266, 21200338220630, 77901645076998, 286615385651970, 1055762834791114, 3893279267979662
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Contribution from Paul Barry (pbarry(AT)wit.ie), Jan 19 2009: (Start)
Hankel transform is 2^C(n+1,2).
Row sums of Riordan array ((1-2x)/(1-x+2x^2),x(1-x)/(1-x+2x^2))^{-1}.
G.f.: 1/(1-2x-2x^2/(1-x-2x^2/(1-x-2x^2/(1-x-2x^2/(1-.... (continued fraction).
First column of Riordan array ((1-x)/(1+x+2x^2),x/(1+x+2x^2))^{-1}. (End)
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LINKS
| M. Bousquet-Melou and M. Mishna, 2008. Walks with small steps in the quarter plane, ArXiv 0810.4387.
A. Bostan and M. Kauers, 2008. Automatic Classification of Restricted Lattice Walks, ArXiv 0811.2899.
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FORMULA
| Conjecture: (n+1)*a(n)-3*(2n+1)*a(n-1) +(n+10)*a(n-2) +28(n-2)*a(n-3)=0 . - R. J. Mathar, Dec 08 2011
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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[i, -1 + j, -1 + n] + aux[1 + i, j, -1 + n] + aux[1 + i, 1 + j, -1 + n]]; Table[Sum[aux[i, j, n], {i, 0, n}, {j, 0, n}], {n, 0, 25}]
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CROSSREFS
| Sequence in context: A148459 A081057 A000137 * A193777 A157004 A085139
Adjacent sequences: A151279 A151280 A151281 * A151283 A151284 A151285
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KEYWORD
| nonn,walk
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AUTHOR
| Manuel Kauers (manuel(AT)kauers.de), Nov 18 2008
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