A298078 - OEIS

%I #58 Jul 05 2021 11:59:17

%S -43,-29,-1,41,97,167,251,349,461,587,727,881,1049,1231,1427,1637,

%T 1861,2099,2351,2617,2897,3191,3499,3821,4157,4507,4871,5249,5641,

%U 6047,6467,6901,7349,7811,8287,8777,9281,9799,10331,10877,11437,12011,12599,13201,13817,14447,15091,15749,16421,17107

%N a(n) = 7*n^2 - 7*n - 43.

%H Colin Barker, <a href="/A298078/b298078.txt">Table of n, a(n) for n = 1..1000</a>

%H Charles Kusniec, <a href="/A298078/a298078.jpg">Modularity Study For U(L;C)=7L^2-7L-43</a>

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

%F From _Colin Barker_, Jan 14 2018: (Start)

%F G.f.: -x*(43 - 100*x + 43*x^2) / (1 - x)^3.

%F a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>3. (End)

%F E.g.f.: 43 + exp(x)*(-43 + 7*x^2). - _Stefano Spezia_, Oct 17 2019

%t Array[7 #^2 - 7 # - 43 &, 48] (* _Michael De Vlieger_, Jan 11 2018 *)

%t LinearRecurrence[{3,-3,1},{-43,-29,-1},50] (* _Harvey P. Dale_, Jul 05 2021 *)

%o (PARI) Vec(-x*(43 - 100*x + 43*x^2) / (1 - x)^3 + O(x^60)) \\ _Colin Barker_, Jan 14 2018

%Y Cf. A272077.

%K sign,easy

%O 1,1

%A _Charles Kusniec_, Jan 11 2018