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%I #29 Sep 08 2022 08:44:50
%S 0,2,6,12,24,40,72,126,240,468,960,2002,4248,9048,19320,41190,87648,
%T 185980,393552,830490,1748040,3670464,7690056,16078702,33555024,
%U 69905700,145403232,301990626,626350200,1297438888,2684355480,5547667062,11453247168,23622321228,48676297200,100215904810
%N a(n) = n*(n + ceiling(2^n/12)).
%H Vincenzo Librandi, <a href="/A029929/b029929.txt">Table of n, a(n) for n = 0..1000</a>
%H C. Musès, <a href="http://dx.doi.org/10.1016/S0096-3003(97)00004-0">The dimensional family approach in (hyper)sphere packing...</a>, Applied Math. Computation 88 (1997), pp. 1-26, see p. 7.
%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (5,-6,-6,15,-3,-8,4).
%F a(n) = n*(6+2*(-1)^n+2^n+12*n)/12. G.f.: 2*x*(x^7 -2*x^6 -2*x^5 +x^4 -6*x^3 +3*x^2 +2*x -1) / ((x-1)^3*(x+1)^2*(2*x-1)^2). - _Colin Barker_, Aug 04 2013
%t CoefficientList[Series[2 x (x^7 - 2 x^6 - 2 x^5 + x^4 - 6 x^3 + 3 x^2 + 2 x - 1)/((x - 1)^3 (x + 1)^2 (2 x - 1)^2), {x, 0, 40}], x] (* _Vincenzo Librandi_, Oct 19 2013 *)
%t Table[n(n+Ceiling[2^n/12]),{n,0,40}] (* or *) LinearRecurrence[{5,-6,-6,15,-3,-8,4},{0,2,6,12,24,40,72,126,240},50] (* _Harvey P. Dale_, Sep 05 2020 *)
%o (PARI) a(n) = n*(n + ceil(2^n/12)) \\ _Michel Marcus_, May 11 2013
%o (Magma) [n*(n + Ceiling(2^n/12)): n in [0..40]]; // _Vincenzo Librandi_, Oct 19 2013
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_
%E Added more terms, _Joerg Arndt_, May 11 2013
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