A017629 a(n) = 12*n + 9.

9, 21, 33, 45, 57, 69, 81, 93, 105, 117, 129, 141, 153, 165, 177, 189, 201, 213, 225, 237, 249, 261, 273, 285, 297, 309, 321, 333, 345, 357, 369, 381, 393, 405, 417, 429, 441, 453, 465, 477, 489, 501, 513, 525, 537, 549, 561, 573, 585, 597, 609, 621, 633

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

Numbers k such that k mod 2 = (k+1) mod 3 = 1 and (k+2) mod 4 != 1. - Klaus Brockhaus, Jun 15 2004

For n > 3, the number of squares on the infinite 3-column chessboard at <= n knight moves from any fixed point. - Ralf Stephan, Sep 15 2004

A016946 is the subsequence of squares (for n = 3*k*(k+1) = A028896(k), then a(n) = (6k+3)^2 = A016946(k)). - Bernard Schott, Apr 05 2021

Links

• Tanya Khovanova, Recursive Sequences.
• Index entries for linear recurrences with constant coefficients, signature (2,-1).

Crossrefs

Subsequences include A072065, A016945, A016813, A008585, and A005408.

Cf. A008594, A017533, A017545, A017137, A004767, A001019, A028896, A016946, A089911.

Programs

Haskell

a017629 = (+ 9) . (* 12)  -- Reinhard Zumkeller, Jul 05 2013

Mathematica

12*Range[0,200]+9 (* Vladimir Joseph Stephan Orlovsky, Feb 19 2011 *)
LinearRecurrence[{2,-1},{9,21},60] (* Harvey P. Dale, Apr 14 2019 *)

PARI

a(n)=12*n+9 \\ Charles R Greathouse IV, Jul 10 2016

Sage

[i+9 for i in range(525) if gcd(i,12) == 12] # Zerinvary Lajos, May 21 2009

Formula

a(n) = 6*(4*n+1) - a(n-1) (with a(0)=9). - Vincenzo Librandi, Dec 17 2010

A089911(2*a(n)) = 4. - Reinhard Zumkeller, Jul 05 2013

G.f.: (9 + 3*x)/(1 - x)^2. - Alejandro J. Becerra Jr., Jul 08 2020

Sum_{n>=0} (-1)^n/a(n) = (Pi + log(3-2*sqrt(2)))/(12*sqrt(2)). - Amiram Eldar, Dec 12 2021

E.g.f.: 3*exp(x)*(3 + 4*x). - Stefano Spezia, Feb 25 2023