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a(n) = 2*n^2 + n - 7.
13

%I #12 Mar 25 2021 13:04:41

%S -7,-4,3,14,29,48,71,98,129,164,203,246,293,344,399,458,521,588,659,

%T 734,813,896,983,1074,1169,1268,1371,1478,1589,1704,1823,1946,2073,

%U 2204,2339,2478,2621,2768,2919,3074,3233,3396,3563,3734,3909,4088,4271,4458,4649

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

%H G. C. Greubel, <a href="/A100041/b100041.txt">Table of n, a(n) for n = 0..5000</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).

%F A100035(a(n)) = 5 for n>3.

%F a(n) = A014105(n) - 7 = A084849(n) - 8 = A100040(n) - 2.

%F From _G. C. Greubel_, Jul 15 2017: (Start)

%F G.f.: (7 - 17 x + 6 x^2)/(-1 + x)^3.

%F E.g.f.: (2*x^2 + 3*x - 7)*exp(x). (End)

%t Table[2*n^2 + n - 7, {n, 0, 50}] (* _G. C. Greubel_, Jul 15 2017 *)

%t LinearRecurrence[{3,-3,1},{-7,-4,3},50] (* _Harvey P. Dale_, Mar 25 2021 *)

%o (PARI) a(n)=2*n^2+n-7 \\ _Charles R Greathouse IV_, Jun 17 2017

%Y Cf. A100036, A100037, A100038, A100039.

%K sign,easy

%O 0,1

%A _Reinhard Zumkeller_, Oct 31 2004