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%I #22 Dec 17 2023 16:20:37
%S 0,6,48,126,240,390,576,798,1056,1350,1680,2046,2448,2886,3360,3870,
%T 4416,4998,5616,6270,6960,7686,8448,9246,10080,10950,11856,12798,
%U 13776,14790,15840,16926,18048,19206,20400,21630,22896,24198,25536,26910,28320,29766
%N 6 times octagonal numbers: a(n) = 6*n*(3*n-2).
%H G. C. Greubel, <a href="/A153796/b153796.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) = 18*n^2 - 12*n = 6*A000567(n) = 3*A139267(n) = 2*A152751(n).
%F a(n) = a(n-1) + 36*n - 30 (with a(0)=0). - _Vincenzo Librandi_, Dec 15 2010
%F From _G. C. Greubel_, Aug 29 2016: (Start)
%F a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>2.
%F G.f.: 6*x*(1 + 5*x)/(1 - x)^3.
%F E.g.f.: 6*x*(1 + 3*x)*exp(x). (End)
%p A153796:=n->6*n*(3*n-2): seq(A153796(n), n=0..60); # _Wesley Ivan Hurt_, Aug 29 2016
%t s=0;lst={s};Do[s+=n;AppendTo[lst,s],{n,6,8!,36}];lst (* _Vladimir Joseph Stephan Orlovsky_, Apr 03 2009 *)
%t Table[6*n*(3*n-2), {n,0,25}] (* or *) LinearRecurrence[{3,-3,1}, {0,6,48}, 25] (* _G. C. Greubel_, Aug 29 2016 *)
%t 6*PolygonalNumber[8,Range[0,50]] (* _Harvey P. Dale_, Dec 17 2023 *)
%o (Magma) [6*n*(3*n-2): n in [0..60]]; // _Wesley Ivan Hurt_, Aug 29 2016
%o (PARI) a(n)=6*n*(3*n-2) \\ _Charles R Greathouse IV_, Aug 29 2016
%Y Cf. A000567, A139267, A152751.
%K easy,nonn
%O 0,2
%A _Omar E. Pol_, Jan 19 2009
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