OFFSET
0,1
COMMENTS
Numbers whose digital root is 3. - Cino Hilliard, Dec 26 2006
a(n)^2 = A017198(n). - Reinhard Zumkeller, Jul 13 2010
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
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
a(n) = a(n-1) + 9.
a(n) = 3*A016777(n).
From Philippe Deléham, Mar 10 2004: (Start)
Sum_{n>=0} (-1)^n / a(n) = (Pi / sqrt(3) + log(2))/9.
G.f.: 3*(1+2*x)/(1-x)^2. (End)
a(n) = 3*(6*n-1) - a(n-1) with a(0)=3. - Vincenzo Librandi, Nov 20 2010
E.g.f.: 3*(1 + 3*x)*exp(x). - G. C. Greubel, Dec 03 2019
MAPLE
seq(9*n+3, n=0..60); # G. C. Greubel, Dec 03 2019
MATHEMATICA
3*(3*Range[60] -2) (* G. C. Greubel, Dec 03 2019 *)
LinearRecurrence[{2, -1}, {3, 12}, 80] (* or *) NestList[#+9&, 3, 80] (* Harvey P. Dale, Jan 22 2023 *)
PROG
(PARI) vector(60, n, 3*(3*n-2) ) \\ G. C. Greubel, Dec 03 2019
(Sage) [i+3 for i in range(480) if gcd(i, 9) == 9] # Zerinvary Lajos, May 20 2009
(Haskell)
a017197 = (+ 3) . (* 9)
a017197_list = [3, 12 ..] -- Reinhard Zumkeller, Jun 04 2015
(Magma) [9*n+3: n in [0..60]]; // G. C. Greubel, Dec 03 2019
(GAP) List([0..60], n-> 9*n+3); # G. C. Greubel, Dec 03 2019
CROSSREFS
Cf. sequences with general form q*(q*n+1): A016825 (q=2), this sequence (q=3), A119413 (q=4), ... - Vladimir Joseph Stephan Orlovsky, Feb 16 2009
Cf. A016777.
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
More terms from Cino Hilliard, Dec 26 2006
STATUS
approved