OFFSET
0,1
COMMENTS
General form: (q*n-1)*q, cf. A017233 (q=3), A098502 (q=4). - Vladimir Joseph Stephan Orlovsky, Feb 16 2009
Numbers whose digital root is 6; that is, A010888(a(n)) = 6. (Ball essentially says that Iamblichus (circa 350) announced that a number equal to the sum of three integers 3n, 3n - 1, and 3n - 2 has 6 as what is now called the number's digital root.) - Rick L. Shepherd, Apr 01 2014
REFERENCES
W. W. R. Ball, A Short Account of the History of Mathematics, Sterling Publishing Company, Inc., 2001 (Facsimile Edition) [orig. pub. 1912], pages 110-111.
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..5000
Tanya Khovanova, Recursive Sequences.
Luis Manuel Rivera, Integer sequences and k-commuting permutations, arXiv preprint arXiv:1406.3081 [math.CO], 2014-2015.
Index entries for linear recurrences with constant coefficients, signature (2,-1).
FORMULA
G.f.: 3*(2+x)/(x-1)^2 . - R. J. Mathar, Mar 20 2018
Sum_{n>=0} (-1)^n/a(n) = sqrt(3)*Pi/27 - log(2)/9. - Amiram Eldar, Dec 12 2021
MATHEMATICA
Range[6, 1000, 9] (* Vladimir Joseph Stephan Orlovsky, May 28 2011 *)
LinearRecurrence[{2, -1}, {6, 15}, 60] (* Harvey P. Dale, Feb 01 2014 *)
PROG
(Magma) [9*n+6: n in [0..60]]; // Vincenzo Librandi, Jul 24 2011
(PARI) a(n)=9*n+6 \\ Charles R Greathouse IV, Oct 07 2015
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
David J. Horn and Laura Krebs Gordon (lkg615(AT)verizon.net), 1985
STATUS
approved