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A139267 Twice octagonal numbers: 2*n*(3*n-2).

%I A139267 #47 Sep 27 2024 02:50:45
%S A139267 0,2,16,42,80,130,192,266,352,450,560,682,816,962,1120,1290,1472,1666,
%T A139267 1872,2090,2320,2562,2816,3082,3360,3650,3952,4266,4592,4930,5280,
%U A139267 5642,6016,6402,6800,7210,7632,8066,8512,8970,9440,9922
%N A139267 Twice octagonal numbers: 2*n*(3*n-2).
%C A139267 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
%H A139267 G. C. Greubel, <a href="/A139267/b139267.txt">Table of n, a(n) for n = 0..1000</a>
%H A139267 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A139267 a(n) = 2*A000567(n) = 6*n^2 - 4*n = 2*n*(3*n - 2).
%F A139267 a(n) = a(n-1) + 12*n - 10, with n>0, a(0)=0. - _Vincenzo Librandi_, Aug 03 2010
%F A139267 G.f.: x*(2+10*x)/(1-3*x+3*x^2-x^3). - _Colin Barker_, Jan 06 2012
%F A139267 After 0, a(n) = Sum_{i=0..n-1} (12*i + 2). - _Bruno Berselli_, Sep 11 2013
%F A139267 E.g.f.: 2*x*(1 + 3*x)*exp(x). - _G. C. Greubel_, Sep 18 2019
%p A139267 seq(2*n*(3*n-2), n=0..50); # _G. C. Greubel_, Sep 18 2019
%t A139267 Table[2*n*(3*n-2), {n,0,50}] (* _G. C. Greubel_, Jun 07 2017 *)
%o A139267 (PARI) a(n)=2*n*(3*n-2) \\ _Charles R Greathouse IV_, Oct 07 2015
%o A139267 (Magma) [2*n*(3*n-2): n in [0..50]]; // _G. C. Greubel_, Sep 18 2019
%o A139267 (Sage) [2*n*(3*n-2) for n in (0..50)] # _G. C. Greubel_, Sep 18 2019
%o A139267 (GAP) List([0..50], n-> 2*n*(3*n-2)); # _G. C. Greubel_, Sep 18 2019
%Y A139267 Cf. A000567, A017545.
%Y A139267 Cf. numbers of the form n*(n*k-k+4)/2 listed in A226488 (this sequence is the case k=12).
%K A139267 nonn,easy
%O A139267 0,2
%A A139267 _Omar E. Pol_, May 14 2008, May 19 2008