A239796 a(n) = 7*n^2 + 2*n - 15.

-6, 17, 54, 105, 170, 249, 342, 449, 570, 705, 854, 1017, 1194, 1385, 1590, 1809, 2042, 2289, 2550, 2825, 3114, 3417, 3734, 4065, 4410, 4769, 5142, 5529, 5930, 6345, 6774, 7217, 7674, 8145, 8630, 9129, 9642, 10169, 10710, 11265, 11834, 12417, 13014, 13625, 14250, 14889, 15542, 16209, 16890

Offset

1,1

Comments

Follows the integer values from 1 on the parabola: 7*n^2 + 2*n - 15.

Real roots: (-1 +- sqrt(106))/7. - Wesley Ivan Hurt, Mar 26 2014

The first in the family of parabolas of the form: prime(k+3)*n^2 + prime(k)*n - prime(k+1)*prime(k+2), where k >= 1 (k=1 gives a(n)). - Wesley Ivan Hurt, Mar 26 2014

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Vi Hart, Doodling in Math Class: Connecting Dots (2012) [Video]

Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Formula

a(n) = n * A017005(n) - 15. - Wesley Ivan Hurt, Mar 26 2014

G.f.: -x*(6 - 35*x + 15*x^2)/(1 - x)^3. - Bruno Berselli, Mar 27 2014

Example

For n=3, a(3) = 7*3^2 + 2*3 - 15 = 54; for n=6, a(6) = 7*6^2 + 2*6 - 15 = 249.

Maple

A239796:=n->7*n^2 +2*n - 15; seq(A239796(n), n=1..50); # Wesley Ivan Hurt, Mar 26 2014

Mathematica

Table[7 n^2 + 2 n - 15, {n, 50}] (* Wesley Ivan Hurt, Mar 26 2014 *)
CoefficientList[Series[(6 - 35 x + 15 x^2)/(x - 1)^3, {x, 0, 50}], x] (* Vincenzo Librandi, Mar 29 2014 *)

Prog

(Magma) [7*n^2+2*n-15: n in [1..50]]; // Bruno Berselli, Mar 27 2014
(PARI) a(n)=7*n^2 + 2*n - 15 \\ Charles R Greathouse IV, Jan 21 2016

Crossrefs

Sequence in context: A199113 A297297 A241352 * A231223 A231437 A323358

Adjacent sequences: A239793 A239794 A239795 * A239797 A239798 A239799

Keyword

sign,easy

Author

Katherine Guo, Mar 26 2014

Status

approved