|
| |
|
|
A151334
|
|
Number of walks within N^2 (the first quadrant of Z^2) starting and ending at (0,0) and consisting of 3 n steps taken from {(-1, 0), (0, 1), (1, -1)}
|
|
0
| |
|
|
1, 1, 5, 42, 462, 6006, 87516, 1385670, 23371634, 414315330, 7646001090, 145862174640, 2861142656400, 57468093927120, 1178095925505960, 24584089974896430, 521086299271824330, 11198784501894470250, 243661974372798631650, 5360563436201569896300, 119115896614816702500900
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,3
|
|
|
LINKS
| M. Bousquet-Melou and M. Mishna, 2008. Walks with small steps in the quarter plane, ArXiv 0810.4387.
|
|
|
FORMULA
| Apparently a(n)=A005789(n), n>0. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Dec 13 2008]
G.f.: (1/30)*(1/x-27)*(9*hypergeom([1/3, 2/3],[1],27*x)+(216*x+1)*hypergeom([4/3, 5/3],[2],27*x))-1/(3x) [From Mark van Hoeij (hoeij(AT)math.fsu.edu), Oct 14 2009]
|
|
|
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]]; Table[aux[0, 0, 3 n], {n, 0, 25}]
|
|
|
CROSSREFS
| Sequence in context: A126765 A024492 A005789 * A102693 A052654 A108398
Adjacent sequences: A151331 A151332 A151333 * A151335 A151336 A151337
|
|
|
KEYWORD
| nonn,walk
|
|
|
AUTHOR
| Manuel Kauers (manuel(AT)kauers.de), Nov 18 2008
|
| |
|
|
