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Search: id:A060774
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| A060774 |
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a(n)= number of lattice paths from (0,0,0) to (n,n,n) along the cracks on the surface of a Rubik-ized n X n X n cube so that no step increases distance from goal. |
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+0
1
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| 6, 54, 384, 2550, 16506, 105840, 677088, 4335606, 27829230, 179161554, 1156987728, 7493841264, 48672149064, 316920674880, 2068273848384, 13525486999542, 88612412883030, 581503640659830, 3821691744347400
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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3-dimensional version of block-walking (0,0) to (n,n) in binomial(2n,n) ways.
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REFERENCES
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W. Li and E.T.H. Wang, "A Bug's Shortest Path on a Cube", Mathematics Magazine, vol. 58, no. 4, Sept. 1985
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FORMULA
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6*(binomial(3n, n)-binomial(2n, n))
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EXAMPLE
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a(1)=6: XYZ, XZY, YXZ, YZX, ZXY, ZYX
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PROGRAM
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(PARI) j=[]; for(n=1, 50, j=concat(j, 6*(binomial(3*n, n)-binomial(2*n, n)))); j
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CROSSREFS
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Adjacent sequences: A060771 A060772 A060773 this_sequence A060775 A060776 A060777
Sequence in context: A097645 A072368 A116138 this_sequence A043026 A125837 A065088
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KEYWORD
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nonn,easy
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AUTHOR
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Len Smiley (smiley(AT)math.uaa.alaska.edu), Apr 25 2001
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EXTENSIONS
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More terms from Jason Earls (zevi_35711(AT)yahoo.com), Jul 03 2001
Corrected by Franklin T. Adams-Watters and T. D. Noe (noe(AT)sspectra.com), Oct 25 2006
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