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A028881
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a(n) = n^2 - 7.
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7
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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
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OFFSET
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3,1
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COMMENTS
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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
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LINKS
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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).
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FORMULA
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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)
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MATHEMATICA
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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 *)
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PROG
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(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
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CROSSREFS
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Sequence in context: A240651 A282519 A103256 * A294535 A294543 A295956
Adjacent sequences: A028878 A028879 A028880 * A028882 A028883 A028884
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KEYWORD
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nonn,easy
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AUTHOR
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Patrick De Geest
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STATUS
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approved
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