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%I #38 May 08 2022 17:17:36
%S 0,3,24,63,120,195,288,399,528,675,840,1023,1224,1443,1680,1935,2208,
%T 2499,2808,3135,3480,3843,4224,4623,5040,5475,5928,6399,6888,7395,
%U 7920,8463,9024,9603,10200,10815,11448,12099,12768,13455
%N 3 times octagonal numbers: 3*n*(3*n-2).
%C a(n) also can be represented as n concentric triangles (see example). - _Omar E. Pol_, Aug 21 2011
%H Ivan Panchenko, <a href="/A152751/b152751.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F a(n) = 9*n^2 - 6*n = A000567(n)*3 = A064201(n)/3.
%F a(n) = a(n-1) + 18*n - 15 with n>0, a(0)=0. - _Vincenzo Librandi_, Nov 26 2010
%F G.f.: 3*x*(1+5*x)/(1-x)^3. - _Bruno Berselli_, Jan 21 2011
%e From _Omar E. Pol_, Aug 21 2011: (Start)
%e Illustration of initial terms as concentric triangles:
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%e . 3 24 63
%e (End)
%t s=0;lst={s};Do[s+=n;AppendTo[lst,s],{n,3,6!,18}];lst (* _Vladimir Joseph Stephan Orlovsky_, Apr 02 2009 *)
%t 3*PolygonalNumber[8,Range[0,40]] (* _Harvey P. Dale_, May 08 2022 *)
%o (PARI) a(n)=3*n*(3*n-2) \\ _Charles R Greathouse IV_, Sep 24 2015
%Y Cf. A000567, A064201, A139267.
%Y 3 times n-gonal numbers: A045943, A033428, A062741, A094159, A152773, A152759, A152767, A153783, A153448, A153875.
%Y Cf. A033581, A085250, A152734, A194273. - _Omar E. Pol_, Aug 21 2011
%Y Cf. numbers of the form n*(n*k-k+6))/2, this sequence is the case k=18: see Comments lines of A226492.
%K easy,nonn
%O 0,2
%A _Omar E. Pol_, Dec 12 2008
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