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

1,1

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).

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)

Example

(1^3 + 3^3)/2 = 14, ...

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 *)

Prog

(PARI) Vec(2*x*(7*x^2+10*x+7)/(x-1)^4 + O(x^100)) \\ Colin Barker, Jan 17 2015

Crossrefs

Cf. A027575, A173960, A173961, A271636.

Sequence in context: A270704 A200554 A152100 * A200547 A240045 A280396

Adjacent sequences: A173959 A173960 A173961 * A173963 A173964 A173965

Keyword

nonn,easy

Author

Vladimir Joseph Stephan Orlovsky, Mar 03 2010

Status

approved