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%I #77 Feb 25 2023 20:57:39
%S 9,21,33,45,57,69,81,93,105,117,129,141,153,165,177,189,201,213,225,
%T 237,249,261,273,285,297,309,321,333,345,357,369,381,393,405,417,429,
%U 441,453,465,477,489,501,513,525,537,549,561,573,585,597,609,621,633
%N a(n) = 12*n + 9.
%C Numbers k such that k mod 2 = (k+1) mod 3 = 1 and (k+2) mod 4 != 1. - _Klaus Brockhaus_, Jun 15 2004
%C 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
%C 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
%H Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/RecursiveSequences.html">Recursive Sequences</a>.
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1).
%F a(n) = 6*(4*n+1) - a(n-1) (with a(0)=9). - _Vincenzo Librandi_, Dec 17 2010
%F A089911(2*a(n)) = 4. - _Reinhard Zumkeller_, Jul 05 2013
%F G.f.: (9 + 3*x)/(1 - x)^2. - _Alejandro J. Becerra Jr._, Jul 08 2020
%F Sum_{n>=0} (-1)^n/a(n) = (Pi + log(3-2*sqrt(2)))/(12*sqrt(2)). - _Amiram Eldar_, Dec 12 2021
%F E.g.f.: 3*exp(x)*(3 + 4*x). - _Stefano Spezia_, Feb 25 2023
%t 12*Range[0,200]+9 (* _Vladimir Joseph Stephan Orlovsky_, Feb 19 2011 *)
%t LinearRecurrence[{2,-1},{9,21},60] (* _Harvey P. Dale_, Apr 14 2019 *)
%o (Sage) [i+9 for i in range(525) if gcd(i,12) == 12] # _Zerinvary Lajos_, May 21 2009
%o (Haskell)
%o a017629 = (+ 9) . (* 12) -- _Reinhard Zumkeller_, Jul 05 2013
%o (PARI) a(n)=12*n+9 \\ _Charles R Greathouse IV_, Jul 10 2016
%Y Subsequences include A072065, A016945, A016813, A008585, and A005408.
%Y Cf. A008594, A017533, A017545, A017137, A004767, A001019, A028896, A016946, A089911.
%K nonn,easy
%O 0,1
%A _N. J. A. Sloane_
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