A017197 a(n) = 9*n + 3.

3, 12, 21, 30, 39, 48, 57, 66, 75, 84, 93, 102, 111, 120, 129, 138, 147, 156, 165, 174, 183, 192, 201, 210, 219, 228, 237, 246, 255, 264, 273, 282, 291, 300, 309, 318, 327, 336, 345, 354, 363, 372, 381, 390, 399, 408, 417, 426, 435, 444, 453, 462, 471, 480

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

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).

Crossrefs

Cf. A092292, A092293, A092296.

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.

Programs

GAP

List([0..60], n-> 9*n+3); # G. C. Greubel, Dec 03 2019

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

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 *)

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

Formula

a(n) = a(n-1) + 9.

a(n) = 3*A016777(n).

a(n) = A092292(n) + A092293(n) + A092296(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

Extensions

More terms from Cino Hilliard, Dec 26 2006