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A016743
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Even cubes: a(n) = (2*n)^3.
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11
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0, 8, 64, 216, 512, 1000, 1728, 2744, 4096, 5832, 8000, 10648, 13824, 17576, 21952, 27000, 32768, 39304, 46656, 54872, 64000, 74088, 85184, 97336, 110592, 125000, 140608, 157464, 175616, 195112, 216000, 238328, 262144, 287496, 314432
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OFFSET
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0,2
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COMMENTS
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a(n) is also the number of non-degenerate triangles that can be drawn with vertices on a cross with n points on each branch. - James P. B. Hall, Nov 22 2019
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 0..10000
Ana Rechtman, Mars 2022, 1er défi, Images des Mathématiques, CNRS, 2022 (in French).
Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).
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FORMULA
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a(n) = (2*n)^3 = 8*n^3.
G.f.: x*(8+32*x+8*x^2)/(1-4*x+6*x^2-4*x^3+x^4). - Colin Barker, Jan 02 2012
E.g.f.: 8*x*(1 +3*x +x^2)*exp(x). - G. C. Greubel, Sep 15 2018
From Amiram Eldar, Oct 10 2020: (Start)
Sum_{n>=1} 1/a(n) = zeta(3)/8 (A276712).
Sum_{n>=1} (-1)^(n+1)/a(n) = 3*zeta(3)/32. (End)
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MAPLE
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A016743:=n->(2*n)^3: seq(A016743(n), n=0..50); # Wesley Ivan Hurt, Sep 15 2018
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MATHEMATICA
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Range[0, 78, 2]^3 (* Alonso del Arte, Apr 06 2013 *)
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PROG
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(MAGMA) [(2*n)^3: n in [0..50]]; // Vincenzo Librandi, Sep 05 2011
(PARI) a(n) = 8*n^3; \\ Joerg Arndt, Apr 07 2013
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CROSSREFS
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Even bisection of A000578, cf. A016755.
Cf. A016803 (even bisection), A016827 (odd bisection), A033581, A276712.
Sequence in context: A207113 A207393 A207940 * A340695 A086114 A209651
Adjacent sequences: A016740 A016741 A016742 * A016744 A016745 A016746
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane
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STATUS
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approved
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