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 A028881 a(n) = n^2 - 7. 7
 2, 9, 18, 29, 42, 57, 74, 93, 114, 137, 162, 189, 218, 249, 282, 317, 354, 393, 434, 477, 522, 569, 618, 669, 722, 777, 834, 893, 954, 1017, 1082, 1149, 1218, 1289, 1362, 1437, 1514, 1593, 1674, 1757, 1842, 1929, 2018, 2109, 2202, 2297, 2394 (list; graph; refs; listen; history; text; internal format)
 OFFSET 3,1 COMMENTS 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 LINKS G. C. Greubel, Table of n, a(n) for n = 3..1000 Patrick De Geest, Palindromic Quasipronics of the form n(n+x) Index entries for linear recurrences with constant coefficients, signature (3,-3,1). FORMULA a(n) = a(n-1) + 2*n - 1, with a(3)=2. - Vincenzo Librandi, Aug 05 2010 G.f.: x^3*(2+3*x-3*x^2)/(1-x)^3. - Colin Barker, Feb 17 2012 E.g.f.: (1/2)*(2*(x^2 + x -7)*exp(x) + 14 + 12*x + 3*x^2). - G. C. Greubel, Aug 19 2017 From Amiram Eldar, Nov 04 2020: (Start) Sum_{n>=3} 1/a(n) = (8 - sqrt(7)*Pi*cot(sqrt(7)*Pi))/14. Sum_{n>=3} (-1)^(n+1)/a(n) = (-10 + 3*sqrt(7)*Pi*cosec(sqrt(7)*Pi))/42. (End) MATHEMATICA 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 *) LinearRecurrence[{3, -3, 1}, {2, 9, 18}, 50] (* G. C. Greubel, Aug 19 2017 *) PROG (Sage)[lucas_number2(2, n, 3-n) for n in range(2, 49)]# Zerinvary Lajos, Mar 12 2009 (PARI) a(n)=n^2-7 \\ Charles R Greathouse IV, Oct 07 2015 CROSSREFS Sequence in context: A240651 A282519 A103256 * A294535 A294543 A295956 Adjacent sequences:  A028878 A028879 A028880 * A028882 A028883 A028884 KEYWORD nonn,easy AUTHOR STATUS approved

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Last modified May 9 03:06 EDT 2021. Contains 343685 sequences. (Running on oeis4.)