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%I #24 Sep 08 2022 08:45:54
%S 0,2,21,57,110,180,267,371,492,630,785,957,1146,1352,1575,1815,2072,
%T 2346,2637,2945,3270,3612,3971,4347,4740,5150,5577,6021,6482,6960,
%U 7455,7967,8496,9042,9605,10185,10782,11396,12027,12675,13340,14022,14721,15437,16170
%N a(n) = n*(17*n - 13)/2.
%H Vincenzo Librandi, <a href="/A180232/b180232.txt">Table of n, a(n) for n = 0..10000</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F a(n) = n + A051871(n).
%F a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).
%F G.f.: x*(2+15*x)/(1-x)^3. - _R. J. Mathar_, Aug 29 2010
%F E.g.f.: x *(4 + 17*x)*exp(x)/2. - _G. C. Greubel_, Aug 30 2019
%p seq(n*(17*n-13)/2, n=0..40); # _G. C. Greubel_, Aug 30 2019
%t Table[(n(17n-13))/2,{n,0,50}] (* or *) LinearRecurrence[{3,-3,1}, {0,2, 21}, 50] (* _Harvey P. Dale_, Sep 14 2011 *)
%o (PARI) a(n)=1/2*(17*n^2 - 13*n);
%o (Magma) [n*(17*n-13)/2:n in [0..40]]; // _Vincenzo Librandi_, Sep 15 2011
%o (Sage) [n*(17*n-13)/2 for n in (0..40)] # _G. C. Greubel_, Aug 30 2019
%o (GAP) List([0..40], n-> n*(17*n-13)/2); # _G. C. Greubel_, Aug 30 2019
%Y Cf. A051871.
%Y Cf. A226488. [_Bruno Berselli_, Jun 10 2013]
%K nonn,easy
%O 0,2
%A Graziano Aglietti (mg5055(AT)mclink.it), Aug 18 2010
%E More terms from _R. J. Mathar_, Aug 29 2010
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