A149632 Number of walks within N^3 (the first octant of Z^3) starting at (0,0,0) and consisting of n steps taken from {(-1, -1, 0), (-1, 0, 0), (-1, 1, 0), (1, 1, -1), (1, 1, 1)}.

1, 1, 5, 15, 69, 217, 1061, 3923, 18769, 70251, 344439, 1375113, 6672345, 26774511, 131685987, 547441335, 2675440089, 11150256511, 54973175867, 234361582283, 1150370062183, 4910734351821, 24255370311897, 105207580829069, 517932742935529, 2248085587718647, 11119639107178211, 48844808538903903

Offset

0,3

Links

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

A. Bostan and M. Kauers, 2008. Automatic Classification of Restricted Lattice Walks, ArXiv 0811.2899.

Maple

M := ((5*x-1)*(x-1)/(24*x^2+1))^(1/2)*(x*(27*x-7)*(24*x^2+1)*hypergeom([1/2, 1/2], [1], 48*x^2/(24*x^2+1))+(18*x^4-288*x^3+189*x^2-36*x+2)*hypergeom([3/2, 3/2], [2], 48*x^2/(24*x^2+1)))/((24*x^2+1)*(x-1)*(15*x^2-12*x+2)^2) ;
ogf := (x/2 + Int((1/12-Int(M, x))*(15*x^2-12*x+2)/(5*x-1)/((5*x-1)*(x-1))^(1/2), x))/(x/3-x^2);
series(ogf, x=0, 30);  # Mark van Hoeij, Apr 06 2012

Mathematica

aux[i_Integer, j_Integer, k_Integer, n_Integer] := Which[Min[i, j, k, n] < 0 || Max[i, j, k] > n, 0, n == 0, KroneckerDelta[i, j, k, n], True, aux[i, j, k, n] = aux[-1 + i, -1 + j, -1 + k, -1 + n] + aux[-1 + i, -1 + j, 1 + k, -1 + n] + aux[1 + i, -1 + j, k, -1 + n] + aux[1 + i, j, k, -1 + n] + aux[1 + i, 1 + j, k, -1 + n]]; Table[Sum[aux[i, j, k, n], {i, 0, n}, {j, 0, n}, {k, 0, n}], {n, 0, 10}]

Crossrefs

Sequence in context: A149630 A149631 A079569 * A149633 A149634 A149635

Adjacent sequences: A149629 A149630 A149631 * A149633 A149634 A149635

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved