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A151423 Number of walks within N^2 (the first quadrant of Z^2) starting at (0,0), ending on the vertical axis and consisting of 2 n steps taken from {(-1, -1), (-1, 0), (-1, 1), (1, -1), (1, 1)}. 0
1, 3, 28, 355, 5264, 85764, 1488432, 27030861, 507976040, 9804514720, 193339562208, 3880220133244, 79026982569976, 1629698960355600, 33969388149210240, 714666181953790035, 15158444163422689080, 323839596100845917400, 6962822068346268247200, 150567286583848676406480 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
LINKS
M. Bousquet-Mélou and M. Mishna, Walks with small steps in the quarter plane, ArXiv 0810.4387, 2008.
MAPLE
G := Int(Int((2*(1-8*t^2)*hypergeom([3/4, 5/4], [1], 64*t^2*(t^2+1)/(16*t^2+1)^2)
+12*t^2*hypergeom([3/4, 5/4], [2], 64*t^2*(t^2+1)/(16*t^2+1)^2))/(16*t^2+1)^(5/2), t), t)/t^2;
ogf := subs(t=x^(1/2), series(G, t=0, 40)); # Mark van Hoeij, Aug 20 2014
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, 1 + j, -1 + n] + aux[1 + i, -1 + j, -1 + n] + aux[1 + i, j, -1 + n] + aux[1 + i, 1 + j, -1 + n]]; Table[Sum[aux[0, k, 2 n], {k, 0, 2 n}], {n, 0, 25}]
CROSSREFS
Sequence in context: A292845 A212032 A352383 * A161605 A048954 A086569
KEYWORD
nonn,walk
AUTHOR
Manuel Kauers, Nov 18 2008
STATUS
approved

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Last modified June 19 00:02 EDT 2024. Contains 373490 sequences. (Running on oeis4.)