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A174029 a(n) = 3*(3*n+1)*(5 - (-1)^n)/4.

%I A174029 #25 Sep 08 2022 08:45:51
%S A174029 3,18,21,45,39,72,57,99,75,126,93,153,111,180,129,207,147,234,165,261,
%T A174029 183,288,201,315,219,342,237,369,255,396,273,423,291,450,309,477,327,
%U A174029 504,345,531,363,558,381,585,399,612,417,639,435,666,453
%N A174029 a(n) = 3*(3*n+1)*(5 - (-1)^n)/4.
%C A174029 All entries are multiples of 3.
%H A174029 Vincenzo Librandi, <a href="/A174029/b174029.txt">Table of n, a(n) for n = 0..10000</a>
%H A174029 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,2,0,-1).
%F A174029 a(2n) = 18*n + 3 = 3*A016921(n);
%F A174029 a(2n+1) = 27*n + 18 = A124388(n).
%F A174029 a(n) = A064680(3n) + A064680(3n+1) + A064680(3n+2).
%F A174029 G.f.: ( 3 + 18*x + 15*x^2 + 9*x^3 ) / ( (x-1)^2*(1+x)^2 ). - _R. J. Mathar_, Jul 02 2011
%F A174029 a(n) = 2*a(n-2) - a(n-4); a(0)=3, a(1)=18, a(2)=21, a(3)=45. - _Harvey P. Dale_, Mar 19 2015
%F A174029 E.g.f.: (3/4)*(5*(1+3*x)*exp(x) - (1-3*x)*exp(-x)). - _G. C. Greubel_, Nov 02 2018
%t A174029 LinearRecurrence[{0,2,0,-1},{3,18,21,45},60] (* _Harvey P. Dale_, Mar 19 2015 *)
%o A174029 (Magma) [3*(3*n+1)*(5-(-1)^n)/4: n in [0..50]]; // _Vincenzo Librandi_, Aug 05 2011
%o A174029 (PARI) vector(50, n, n--; 3*(3*n+1)*(5-(-1)^n)/4) \\ _G. C. Greubel_, Nov 02 2018
%K A174029 nonn,easy
%O A174029 0,1
%A A174029 _Paul Curtz_, Mar 06 2010