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%I #41 Sep 08 2022 08:45:33
%S 0,2,16,42,80,130,192,266,352,450,560,682,816,962,1120,1290,1472,1666,
%T 1872,2090,2320,2562,2816,3082,3360,3650,3952,4266,4592,4930,5280,
%U 5642,6016,6402,6800,7210,7632,8066,8512,8970,9440,9922
%N Twice octagonal numbers: 2*n*(3*n-2).
%C Sequence found by reading the line from 0, in the direction 0, 2,..., in the square spiral whose vertices are the generalized pentagonal numbers A001318. Opposite numbers to the members of A033580 in the same spiral. - _Omar E. Pol_, Sep 09 2011
%C After 0, a(n) = Sum_{i=0..n-1} (12*i + 2). - _Bruno Berselli_, Sep 11 2013
%H G. C. Greubel, <a href="/A139267/b139267.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) = 2*A000567(n) = 6*n^2 - 4*n = 2*n*(3*n - 2).
%F a(n) = a(n-1) + 12*n - 10, with n>0, a(0)=0. - _Vincenzo Librandi_, Aug 03 2010
%F G.f.: x*(2+10*x)/(1-3*x+3*x^2-x^3). - _Colin Barker_, Jan 06 2012
%F E.g.f.: 2*x*(1 + 3*x)*exp(x). - _G. C. Greubel_, Sep 18 2019
%p seq(2*n*(3*n-2), n=0..50); # _G. C. Greubel_, Sep 18 2019
%t Table[2*n*(3*n-2), {n,0,50}] (* _G. C. Greubel_, Jun 07 2017 *)
%o (PARI) a(n)=2*n*(3*n-2) \\ _Charles R Greathouse IV_, Oct 07 2015
%o (Magma) [2*n*(3*n-2): n in [0..50]]; // _G. C. Greubel_, Sep 18 2019
%o (Sage) [2*n*(3*n-2) for n in (0..50)] # _G. C. Greubel_, Sep 18 2019
%o (GAP) List([0..50], n-> 2*n*(3*n-2)); # _G. C. Greubel_, Sep 18 2019
%Y Cf. A000567, A017545.
%Y Cf. numbers of the form n*(n*k-k+4))/2 listed in A226488 (this sequence is the case k=12).
%K nonn,easy
%O 0,2
%A _Omar E. Pol_, May 14 2008, May 19 2008
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