OFFSET
0,1
COMMENTS
Also the perfect cubes with digital root 8. [Proof: perfect cubes are either of the form (3n)^3 or of the form (3n+1)^3 or of the form (3n+2)^3. These subsets have digital root 9, 1 and 8 respectively.] - R. J. Mathar, Oct 02 2008
REFERENCES
Amarnath Murthy, Fabricating a perfect cube with a given valid digit sum (to be published)
LINKS
Harry J. Smith, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).
FORMULA
a(n) = A016789(n)^3. - Nathaniel Johnston, May 04 2011
G.f.: (8+93*x+60*x^2+x^3)/(1-4*x+6*x^2-4*x^3+x^4). - Colin Barker, Jan 02 2012
a(0)=8, a(1)=125, a(2)=512, a(3)=1331, a(n)=4*a(n-1)-6*a(n-2)+4*a(n-3)-a(n-4). - Harvey P. Dale, Feb 20 2013
Sum_{n>=0} 1/a(n) = -2*Pi^3 / (81*sqrt(3)) + 13*zeta(3)/27. - Amiram Eldar, Oct 02 2020
EXAMPLE
a(4) = (3*4 + 2)^3 = 2744.
a(8) = (3*8 + 2)^3 = 17576.
MATHEMATICA
(3*Range[0, 40]+2)^3 (* or *) LinearRecurrence[{4, -6, 4, -1}, {8, 125, 512, 1331}, 40] (* Harvey P. Dale, Feb 20 2013 *)
PROG
(PARI) { for (n=0, 1000, write("b016791.txt", n, " ", (3*n + 2)^3) ) } \\ Harry J. Smith, Jul 18 2009
(PARI) { b=0; for (n=1, 1000, until (s==8, b++; s=b^3; s-=9*(s\9)); write("b016791.txt", n, " ", b^3) ) } \\ Harry J. Smith, Jul 18 2009
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
More terms from Harry J. Smith, Jul 18 2009
First digital root in proof in comment line corrected. - Ant King, May 01 2013
STATUS
approved