A033430 a(n) = 4*n^3.

0, 4, 32, 108, 256, 500, 864, 1372, 2048, 2916, 4000, 5324, 6912, 8788, 10976, 13500, 16384, 19652, 23328, 27436, 32000, 37044, 42592, 48668, 55296, 62500, 70304, 78732, 87808, 97556, 108000, 119164, 131072, 143748, 157216, 171500, 186624, 202612, 219488

Offset

0,2

Comments

2*a(n) = (2*n)^3 is a perfect cube.

Number of edges of the product of two complete bipartite graphs, each of order 2n, K_n,n x K_n,n - Roberto E. Martinez II, Jan 07 2002

This sequence is related to A049451 by a(n) = n*A049451(n) + sum( A049451(i), i=0..n-1 ) for n>0. - Bruno Berselli, Dec 19 2013

For n>=3, also the detour index of the n-gear graph. - Eric W. Weisstein, Dec 20 2017

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..750

F. Ellermann, Illustration of binomial transforms

Eric Weisstein's World of Mathematics, Detour Index

Eric Weisstein's World of Mathematics, Gear Graph

Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Formula

G.f. 4*x*(1+4*x+x^2)/ (x-1)^4. - R. J. Mathar, Feb 01 2011

From Ilya Gutkovskiy, May 25 2016: (Start)

E.g.f.: 4*x*(1 + 3*x + x^2)*exp(x).

Sum_{n>=1} 1/a(n) = zeta(3)/4. (End)

Product_{n>=1} a(n)/A280089(n) = Pi. - Daniel Suteu, Dec 26 2016

From Bruce J. Nicholson, Dec 07 2019: (Start)

a(n) = 24*A000292(n-1) + 4*n.

a(n) = 2*A007588(n) + 2*n. (End)

Mathematica

4 Range[0, 40]^3 (* Harvey P. Dale, Sep 07 2016 *)
LinearRecurrence[{4, -6, 4, -1}, {0, 4, 32, 108}, 40] (* Harvey P. Dale, Sep 07 2016 *)
Table[4 n^3, {n, 0, 20}] (* Eric W. Weisstein, Dec 20 2017 *)
CoefficientList[Series[(4 x (1 + 4 x + x^2))/(-1 + x)^4, {x, 0, 20}], x] (* Eric W. Weisstein, Dec 20 2017 *)

Prog

(Magma) [4*n^3: n in [0..40]]; // Vincenzo Librandi, Apr 27 2011
(PARI) a(n)=4*n^3 \\ Charles R Greathouse IV, Oct 07 2015

Crossrefs

Cf. A000578, A049451.

Cf. A000292, A007588.

Sequence in context: A211630 A211626 A211627 * A267668 A338322 A239056

Adjacent sequences: A033427 A033428 A033429 * A033431 A033432 A033433

Keyword

nonn,easy

Author

Jeff Burch

Status

approved