A298078 a(n) = 7*n^2 - 7*n - 43.

-43, -29, -1, 41, 97, 167, 251, 349, 461, 587, 727, 881, 1049, 1231, 1427, 1637, 1861, 2099, 2351, 2617, 2897, 3191, 3499, 3821, 4157, 4507, 4871, 5249, 5641, 6047, 6467, 6901, 7349, 7811, 8287, 8777, 9281, 9799, 10331, 10877, 11437, 12011, 12599, 13201, 13817, 14447, 15091, 15749, 16421, 17107

Offset: 1

Author

Charles Kusniec, Jan 11 2018

Keywords

• sign
• easy

Links

• Colin Barker, Table of n, a(n) for n = 1..1000
• Charles Kusniec, Modularity Study For U(L;C)=7L^2-7L-43
• Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Crossrefs

Cf. A272077.

Programs

Mathematica

Array[7 #^2 - 7 # - 43 &, 48] (* Michael De Vlieger, Jan 11 2018 *)
LinearRecurrence[{3,-3,1},{-43,-29,-1},50] (* Harvey P. Dale, Jul 05 2021 *)

PARI

Vec(-x*(43 - 100*x + 43*x^2) / (1 - x)^3 + O(x^60)) \\ Colin Barker, Jan 14 2018

Formula

From Colin Barker, Jan 14 2018: (Start)

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

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

E.g.f.: 43 + exp(x)*(-43 + 7*x^2). - Stefano Spezia, Oct 17 2019