A153875 - OEIS

%I #28 Oct 05 2024 09:40:06

%S 0,3,39,108,210,345,513,714,948,1215,1515,1848,2214,2613,3045,3510,

%T 4008,4539,5103,5700,6330,6993,7689,8418,9180,9975,10803,11664,12558,

%U 13485,14445,15438,16464,17523,18615,19740,20898,22089

%N 3 times 13-gonal (or tridecagonal) numbers: a(n) = 3*n*(11*n - 9)/2.

%H G. C. Greubel, <a href="/A153875/b153875.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) = (33*n^2 - 27*n)/2 = A051865(n)*3.

%F a(n) = a(n-1) + 33*n - 30, with n>0, a(0)=0. - _Vincenzo Librandi_, Dec 14 2010

%F G.f.: 3*x*(1 + 10*x)/(1-x)^3. - _Bruno Berselli_, Jan 21 2011

%F From _G. C. Greubel_, Aug 31 2016: (Start)

%F a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).

%F E.g.f.: (3/2)*x*(2 + 11*x)*exp(x). (End)

%t s=0;lst={s};Do[s+=n;AppendTo[lst,s],{n,3,7!,33}];lst (* _Vladimir Joseph Stephan Orlovsky_, Apr 02 2009 *)

%t LinearRecurrence[{3, -3, 1}, {0, 3, 39}, 25] (* or *) Table[33*n^2 - 27*n)/2, {n,0,25}] (* _G. C. Greubel_, Aug 31 2016 *)

%o (PARI) a(n)=3*n*(11*n-9)/2 \\ _Charles R Greathouse IV_, Oct 07 2015

%Y Cf. A051865, A152997.

%Y 3 times n-gonal numbers: A045943, A033428, A062741, A094159, A152773, A152751, A152759, A152767, A153783, A153448.

%Y Cf. numbers of the form n*(n*k-k+6)/2, this sequence is the case k=33: see Comments lines of A226492.

%K nonn,easy

%O 0,2

%A _Omar E. Pol_, Jan 03 2009