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%I #39 Oct 08 2023 04:45:44
%S -1,15,55,119,207,319,455,615,799,1007,1239,1495,1775,2079,2407,2759,
%T 3135,3535,3959,4407,4879,5375,5895,6439,7007,7599,8215,8855,9519,
%U 10207,10919,11655,12415,13199,14007,14839,15695,16575,17479,18407
%N a(n) = (2*n+1)*(6*n-1).
%H Vincenzo Librandi, <a href="/A179741/b179741.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) = a(n-1) + 24*n + 16.
%F a(n) = 2*a(n-1) - a(n-2) + 16.
%F a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).
%F a(n) = A077591(n+1) + A061037(2*n-1).
%F From _Bruno Berselli_, Jan 25 2011: (Start)
%F G.f.: (-1 +18*x +7*x^2)/(1-x)^3.
%F a(n) = A184005(4*n) (n>0). (End)
%F E.g.f.: (-1 + 16*x + 12*x^2)*exp(x). - _G. C. Greubel_, Jul 22 2017
%F From _Amiram Eldar_, Oct 08 2023: (Start)
%F Sum_{n>=1} 1/a(n) = (3*log(3) - Pi*sqrt(3) + 4)/16.
%F Sum_{n>=1} (-1)^(n+1)/a(n) = (3*Pi - 2*sqrt(3)*log(sqrt(3)+2) - 4)/16. (End)
%t Table[12n^2+4n-1,{n,0,40}] (* or *) LinearRecurrence[{3,-3,1},{-1,15,55},40] (* _Harvey P. Dale_, Dec 17 2013 *)
%o (Magma) [(2*n+1)*(6*n-1): n in [0..50]]; // _Vincenzo Librandi_, Aug 04 2011
%o (PARI) a(n)=(2*n+1)*(6*n-1) \\ _Charles R Greathouse IV_, Jun 17 2017
%Y Cf. A061037, A077591, A184005.
%K sign,easy
%O 0,2
%A _Paul Curtz_, Jan 10 2011
%E Edited by _N. J. A. Sloane_, Jan 12 2011