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%I #11 May 27 2021 15:06:51
%S 14,76,234,536,1030,1764,2786,4144,5886,8060,10714,13896,17654,22036,
%T 27090,32864,39406,46764,54986,64120,74214,85316,97474,110736,125150,
%U 140764,157626,175784,195286,216180,238514,262336,287694,314636,343210
%N Averages of two consecutive odd cubes; a(n) = (n^3+(n+2)^3)/2.
%C (1^3 + 3^3)/2 = 14,..
%H Colin Barker, <a href="/A173962/b173962.txt">Table of n, a(n) for n = 1..1000</a>
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).
%F a(n) = 4*a(n-1)-6*a(n-2)+4*a(n-3)-a(n-4). - _Colin Barker_, Jan 17 2015
%F G.f.: 2*x*(7*x^2+10*x+7) / (x-1)^4. - _Colin Barker_, Jan 17 2015
%t f[n_]:=(n^3+(n+2)^3)/2;Table[f[n],{n,1,6!,2}]
%t Mean/@Partition[Range[1,81,2]^3,2,1] (* _Harvey P. Dale_, Apr 20 2015 *)
%o (PARI) Vec(2*x*(7*x^2+10*x+7)/(x-1)^4 + O(x^100)) \\ _Colin Barker_, Jan 17 2015
%Y Cf. A027575, A173960, A173961.
%K nonn,easy
%O 1,1
%A _Vladimir Joseph Stephan Orlovsky_, Mar 03 2010
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