OFFSET
0,1
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).
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
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 *)
PROG
(Sage) [i+9 for i in range(525) if gcd(i, 12) == 12] # Zerinvary Lajos, May 21 2009
(Haskell)
a017629 = (+ 9) . (* 12) -- Reinhard Zumkeller, Jul 05 2013
(PARI) a(n)=12*n+9 \\ Charles R Greathouse IV, Jul 10 2016
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved