OFFSET
1,3
COMMENTS
n == n^3 mod 9, so the iterated sum of the decimal digits of n and n^3 are equal.
REFERENCES
H. I. Okagbue, M.O.Adamu, S.A. Bishop and A.A. Opanuga, Properties of Sequences Generated by Summing the Digits of Cubed Positive Integers, Indian Journal Of Natural Sciences, Vol. 6 / Issue 32 / October 2015
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (1,0,1,-1).
FORMULA
G.f.: x^2*(1+7*x+x^2) / ((1+x+x^2)*(x-1)^2). - R. J. Mathar, Oct 08 2011
From Wesley Ivan Hurt, Jun 14 2016: (Start)
a(n) = a(n-1) + a(n-3) - a(n-4) for n>4.
a(n) = 3*n-3+2*cos(2*n*Pi/3)+2*sin(2*n*Pi/3)/sqrt(3).
a(3k) = 9k-1, a(3k-1) = 9k-8, a(3k-2) = 9k-9. (End)
a(n) -a(n-1) = A105395(n+1), n>1. - R. J. Mathar, Jul 19 2024
MAPLE
A054966:=n->3*n-3+2*cos(2*n*Pi/3)+2*sin(2*n*Pi/3)/sqrt(3): seq(A054966(n), n=1..100); # Wesley Ivan Hurt, Jun 14 2016
MATHEMATICA
Select[Range[0, 200], MemberQ[{0, 1, 8}, Mod[#, 9]] &] (* Wesley Ivan Hurt, Jun 14 2016 *)
LinearRecurrence[{1, 0, 1, -1}, {0, 1, 8, 9}, 100] (* Vincenzo Librandi, Jun 15 2016 *)
PROG
(Magma) [n : n in [0..200] | n mod 9 in [0, 1, 8]]; // Wesley Ivan Hurt, Jun 14 2016
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Henry Bottomley, May 24 2000
STATUS
approved