A173962 Averages of two consecutive odd cubes; a(n) = (n^3 + (n+2)^3)/2.
14, 76, 234, 536, 1030, 1764, 2786, 4144, 5886, 8060, 10714, 13896, 17654, 22036, 27090, 32864, 39406, 46764, 54986, 64120, 74214, 85316, 97474, 110736, 125150, 140764, 157626, 175784, 195286, 216180, 238514, 262336, 287694, 314636, 343210, 373464, 405446
Offset: 1
Examples
(1^3 + 3^3)/2 = 14, ...
Links
- Colin Barker, Table of n, a(n) for n = 1..1000
- Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).
Programs
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Mathematica
f[n_]:=(n^3+(n+2)^3)/2;Table[f[n],{n,1,6!,2}] Mean/@Partition[Range[1,81,2]^3,2,1] (* Harvey P. Dale, Apr 20 2015 *) -
PARI
Vec(2*x*(7*x^2+10*x+7)/(x-1)^4 + O(x^100)) \\ Colin Barker, Jan 17 2015
Formula
From Colin Barker, Jan 17 2015: (Start)
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4).
G.f.: 2*x*(7*x^2+10*x+7)/(x-1)^4. (End)
From Elmo R. Oliveira, Aug 23 2025: (Start)
a(n) = 2*n*(4*n^2 + 3) = A271636(n)/2.
E.g.f.: 2*exp(x)*x*(7 + 12*x + 4*x^2). (End)