A016827 -id:A016827 - cp's OEIS frontend

A016743 Even cubes: a(n) = (2*n)^3.

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

Offset: 0

N. J. A. Sloane

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

Vincenzo Librandi, Table of n, a(n) for n = 0..10000
Hilko Koning, 216 neodymium magnets for n=3.
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).

Even bisection of A000578, cf. A016755.

Cf. A016803 (even bisection), A016827 (odd bisection), A033581, A276712.

[(2*n)^3: n in [0..50]]; // Vincenzo Librandi, Sep 05 2011

A016743:=n->(2*n)^3: seq(A016743(n), n=0..50); # Wesley Ivan Hurt, Sep 15 2018

Range[0, 78, 2]^3 (* Alonso del Arte, Apr 06 2013 *)

a(n) = 8*n^3; \\ Joerg Arndt, Apr 07 2013

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)

A016830 a(n) = (4*n+2)^6.

Original entry on oeis.org

64, 46656, 1000000, 7529536, 34012224, 113379904, 308915776, 729000000, 1544804416, 3010936384, 5489031744, 9474296896, 15625000000, 24794911296, 38068692544, 56800235584, 82653950016, 117649000000, 164206490176, 225199600704, 304006671424, 404567235136, 531441000000

Offset: 0

N. J. A. Sloane

Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).

Cf. A016758, A016825, A016826, A016827.

(4*Range[0,20]+2)^6 (* or *) LinearRecurrence[{7,-21,35,-35,21,-7,1},{64,46656,1000000,7529536,34012224,113379904,308915776},20] (* Harvey P. Dale, Oct 14 2012 *)

a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7). - Harvey P. Dale, Oct 14 2012
From Amiram Eldar, Jul 07 2022: (Start)
a(n) = A016825(n)^6 = A016826(n)^3 = A016827(n)^2 = 64*A016758(n).
Sum_{n>=0} 1/a(n) = Pi^6/61440. (End)

A017115 a(n) = (8*n + 4)^3.

Original entry on oeis.org

64, 1728, 8000, 21952, 46656, 85184, 140608, 216000, 314432, 438976, 592704, 778688, 1000000, 1259712, 1560896, 1906624, 2299968, 2744000, 3241792, 3796416, 4410944, 5088448, 5832000, 6644672, 7529536, 8489664, 9528128, 10648000, 11852352, 13144256, 14526784, 16003008

Offset: 0

N. J. A. Sloane

Vincenzo Librandi, Table of n, a(n) for n = 0..10000
Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Cf. A002117, A016755, A016827, A017113.

[(8*n+4)^3: n in [0..35] ]; // Vincenzo Librandi, Jul 21 2011

LinearRecurrence[{4, -6, 4, -1},{64, 1728, 8000, 21952},24] (* Ray Chandler, Aug 04 2015 *)

G.f.: 64*(1+x)*(x^2 + 22*x + 1)/(x-1)^4. - R. J. Mathar, Jul 14 2016
From Amiram Eldar, Apr 25 2023: (Start)
a(n) = A017113(n)^3.
a(n) = 2^3*A016827(n) = 2^6*A016755(n).
Sum_{n>=0} 1/a(n) = 7*zeta(3)/512.
Sum_{n>=0} (-1)^n/a(n) = Pi^3/2048. (End)
E.g.f.: 64*exp(x)*(1 + 26*x + 36*x^2 + 8*x^3). - Stefano Spezia, May 27 2025

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A016743 Even cubes: a(n) = (2*n)^3.

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A016830 a(n) = (4*n+2)^6.

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A017115 a(n) = (8*n + 4)^3.

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