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%I #32 Dec 11 2024 00:26:16
%S 18,45,72,99,126,153,180,207,234,261,288,315,342,369,396,423,450,477,
%T 504,531,558,585,612,639,666,693,720,747,774,801,828,855,882,909,936,
%U 963,990,1017,1044,1071,1098,1125,1152,1179,1206,1233,1260,1287,1314,1341,1368
%N a(n) = 27*n + 18.
%C Second differences of dodecahedral numbers (A006566).
%C Also, first differences of dodecahedral gnomic numbers (A093485); a(n+1) - a(n) = 27.
%H Vincenzo Librandi, <a href="/A124388/b124388.txt">Table of n, a(n) for n = 0..10000</a>
%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) = 9*A016789(n).
%F G.f.: 9*(2 + x)/(x-1)^2. - _R. J. Mathar_, Jul 02 2011
%F From _Elmo R. Oliveira_, Dec 08 2024: (Start)
%F E.g.f.: 9*exp(x)*(2 + 3*x).
%F a(n) = 2*a(n-1) - a(n-2) for n > 1. (End)
%t Range[18, 7000, 27] (* _Vladimir Joseph Stephan Orlovsky_, Jul 13 2011 *)
%o (Magma) [27*n+18: n in [0..50]]; // _Vincenzo Librandi_, Sep 29 2011
%o (PARI) for(n=0, 1e2, print1(27*n+18, ", ")) \\ _Felix Fröhlich_, Jul 07 2014
%Y Cf. A006566, A016789, A093485.
%K nonn,easy
%O 0,1
%A _Reinhard Zumkeller_, Oct 30 2006