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3n and 2n, alternating.
6

%I #45 Sep 02 2024 04:28:17

%S 3,4,9,8,15,12,21,16,27,20,33,24,39,28,45,32,51,36,57,40,63,44,69,48,

%T 75,52,81,56,87,60,93,64,99,68,105,72,111,76,117,80,123,84,129,88,135,

%U 92,141,96,147,100,153,104,159,108,165,112,171,116,177,120,183

%N 3n and 2n, alternating.

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,2,0,-1).

%F a(n) = n*(2 + (n mod 2)).

%F a(2*n) = 6*n + 3 = A016945(n). - _Paul Curtz_, Nov 23 2008

%F a(2*n+1) = A008586(n+1).

%F From _R. J. Mathar_, Apr 08 2009: (Start)

%F G.f.: x*(3+4*x+3*x^2)/((x-1)^2*(1+x)^2).

%F a(n) = 2*a(n-2) - a(n-4). (End)

%F a(n) = Sum_{d|n} mu(d)*sigma(2*n/d). - _Benoit Cloitre_, Oct 18 2009

%F a(n) = n*(5-(-1)^n)/2. - _Wesley Ivan Hurt_, May 14 2014

%t Table[n(2 + Mod[n, 2]), {n, 50}]

%o (PARI) a(n)=sumdiv(n,d,moebius(d)*sigma(2*n/d)) \\ _Benoit Cloitre_, Oct 18 2009

%Y Cf. A118402 (first differences).

%K nonn,easy

%O 1,1

%A _Zak Seidov_, May 19 2005

%E More terms from _Michel Marcus_, May 17 2014