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A028881 a(n) = n^2 - 7. 7

%I

%S 2,9,18,29,42,57,74,93,114,137,162,189,218,249,282,317,354,393,434,

%T 477,522,569,618,669,722,777,834,893,954,1017,1082,1149,1218,1289,

%U 1362,1437,1514,1593,1674,1757,1842,1929,2018,2109,2202,2297,2394

%N a(n) = n^2 - 7.

%C a(n), n>=0, with a(0) = -7, a(1) = -6 and a(2) = -3, gives the values for a*c of indefinite binary quadratic forms [a, b, c] of discriminant D = 28 for b = 2*n. In general D = b^2 - 4*a*c > 0 and the form [a, b, c] is a*x^2 + b*x*y + c*y^2. - _Wolfdieter Lang_, Aug 16 2013

%H G. C. Greubel, <a href="/A028881/b028881.txt">Table of n, a(n) for n = 3..1000</a>

%H Patrick De Geest, <a href="http://www.worldofnumbers.com/consemor.htm">Palindromic Quasipronics of the form n(n+x)</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) + 2*n - 1, with a(3)=2. - _Vincenzo Librandi_, Aug 05 2010

%F G.f.: x^3*(2+3*x-3*x^2)/(1-x)^3. - _Colin Barker_, Feb 17 2012

%F E.g.f.: (1/2)*(2*(x^2 + x -7)*exp(x) + 14 + 12*x + 3*x^2). - _G. C. Greubel_, Aug 19 2017

%F From _Amiram Eldar_, Nov 04 2020: (Start)

%F Sum_{n>=3} 1/a(n) = (8 - sqrt(7)*Pi*cot(sqrt(7)*Pi))/14.

%F Sum_{n>=3} (-1)^(n+1)/a(n) = (-10 + 3*sqrt(7)*Pi*cosec(sqrt(7)*Pi))/42. (End)

%t s=0;lst={};Do[s+=n;If[(s-7)>0,AppendTo[lst,s-7]],{n,1,6!,2}];lst (* _Vladimir Joseph Stephan Orlovsky_, May 25 2009 *)

%t LinearRecurrence[{3,-3,1}, {2,9,18}, 50] (* _G. C. Greubel_, Aug 19 2017 *)

%o (Sage)[lucas_number2(2,n,3-n) for n in range(2,49)]# _Zerinvary Lajos_, Mar 12 2009

%o (PARI) a(n)=n^2-7 \\ _Charles R Greathouse IV_, Oct 07 2015

%K nonn,easy

%O 3,1

%A _Patrick De Geest_

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Last modified April 13 18:46 EDT 2021. Contains 342939 sequences. (Running on oeis4.)