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A064036
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Number of walks of length n on cubic lattice, starting at origin, staying in first (nonnegative) octant.
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2
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1, 3, 12, 51, 234, 1110, 5460, 27405, 140490, 729918, 3845016, 20447658, 109801692, 593806356, 3234529584, 17715445605, 97567971930, 539701180590, 2998595422680
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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LINKS
| R. K. Guy, Catwalks, Sandsteps and Pascal Pyramids, J. Integer Seqs., Vol. 3 (2000), #00.1.6
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FORMULA
| a(n) =sum_j[C(n, j)B(j)B(j+1)B(n-j)] where B(k)=C(k, [k/2])=A001405(k)
E.g.f.: (BesselI(0, 2*x)+BesselI(1, 2*x))^3. - Vladeta Jovovic (vladeta(AT)eunet.rs), Apr 28 2003
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EXAMPLE
| a(2)=12 since a(1) is obviously 3 and from each of these three positions there are four possible steps which remain in the first octant.
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CROSSREFS
| Cf. A064037. The two- and one-dimensional equivalents are A005566 and A001405. With no restriction on the walks, the number is 6^n, i.e. A000400.
Sequence in context: A151188 A151189 A199875 * A195255 A125187 A151190
Adjacent sequences: A064033 A064034 A064035 * A064037 A064038 A064039
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KEYWORD
| nonn
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AUTHOR
| Henry Bottomley (se16(AT)btinternet.com), Aug 23 2001
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