A078618 a(n) = floor(average of first n cubes).

1, 4, 12, 25, 45, 73, 112, 162, 225, 302, 396, 507, 637, 787, 960, 1156, 1377, 1624, 1900, 2205, 2541, 2909, 3312, 3750, 4225, 4738, 5292, 5887, 6525, 7207, 7936, 8712, 9537, 10412, 11340, 12321, 13357, 14449, 15600, 16810, 18081, 19414, 20812, 22275

Offset

1,2

Links

Table of n, a(n) for n=1..44.

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

Formula

a(n) = floor((1/n)(Sum_{i=1..n} i^3) = floor(n*(n+1)^2/4).

G.f.: x*(1+x+x^4+3*x^2) / ( (1+x)*(x^2+1)*(x-1)^4 ). - R. J. Mathar, Feb 20 2011

Example

a(3) = floor((1 + 8 + 27)/3) = 12.

Maple

ZL:=n->sum(i^3, i=1..n): a:=n->floor(numer(ZL(n))/n): seq(a(n), n=1..44); # Zerinvary Lajos, Mar 28 2007

Mathematica

s = 0; a = {}; For[i = 1, i <= 100, i++, s = s + i^3; a = Append[a, Floor[(1/i) s]]]; a

Prog

(PARI) a(n)=n*(n^2+2*n+1)\4 \\ Charles R Greathouse IV, Oct 07 2015

Crossrefs

Cf. A000537.

Sequence in context: A008186 A008264 A000297 * A246988 A304843 A062883

Adjacent sequences: A078615 A078616 A078617 * A078619 A078620 A078621

Keyword

easy,nonn

Author

Joseph L. Pe, Dec 10 2002

Status

approved