A164579 Integer averages of halves of first cubes of natural numbers (n^3)/2 for some n.

6, 56, 81, 198, 480, 578, 950, 1656, 1875, 2646, 3968, 4356, 5670, 7800, 8405, 10406, 13536, 14406, 17238, 21560, 22743, 26550, 32256, 33800, 38726, 46008, 47961, 54150, 63200, 65610, 73206, 84216, 87131, 96278, 109440, 112908, 123750, 139256

Offset

1,1

Comments

Also, integers of the form (1/8)*n*(n+1)^2 for some n. - Zak Seidov, Aug 17 2009

Links

Table of n, a(n) for n=1..38.

Index entries for linear recurrences with constant coefficients, signature (1,0,3,-3,0,-3,3,0,1,-1).

Formula

G.f.: ( x*(6+50*x+25*x^2+99*x^3+132*x^4+23*x^5+39*x^6+10*x^7) ) / ( (1+x+x^2)^3*(x-1)^4 ). - R. J. Mathar, Jan 25 2011

Example

1/2, 9/4, 6, 25/2, 45/2, 147/4, 56, 81, ...

Mathematica

s=0; lst={}; Do[a=(s+=(n^3)/2)/n; If[Mod[a, 1]==0, AppendTo[lst, a]], {n, 3*5!}]; lst
LinearRecurrence[{1, 0, 3, -3, 0, -3, 3, 0, 1, -1}, {6, 56, 81, 198, 480, 578, 950, 1656, 1875, 2646}, 40] (* Harvey P. Dale, Jul 26 2017 *)
Module[{nn=200, ac}, ac=Accumulate[Range[nn]^3/2]; Select[#[[1]]/#[[2]]&/@ Thread[{ac, Range[nn]}], IntegerQ]] (* Harvey P. Dale, Jan 28 2020 *)

Prog

(PARI) forstep(n=3, 150, [4, 1, 3], print1(n*(n+1)^2>>3, ", ")); \\ Charles R Greathouse IV, Nov 02 2009

Crossrefs

Cf. A050248, A051456, A078617, A078618, A136116, A154293, A164576, A164577, A164578

Sequence in context: A335199 A137033 A045526 * A137034 A177059 A345473

Adjacent sequences: A164576 A164577 A164578 * A164580 A164581 A164582

Keyword

nonn,easy

Author

Vladimir Joseph Stephan Orlovsky, Aug 16 2009

Status

approved