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 A033430 a(n) = 4*n^3. 17
 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 (list; graph; refs; listen; history; text; internal format)
 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 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. Sequence in context: A211630 A211626 A211627 * A267668 A239056 A088658 Adjacent sequences:  A033427 A033428 A033429 * A033431 A033432 A033433 KEYWORD nonn,easy AUTHOR STATUS approved

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Last modified May 24 18:34 EDT 2019. Contains 323534 sequences. (Running on oeis4.)