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
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
KEYWORD
sign,easy
AUTHOR
Katherine Guo, Mar 26 2014
STATUS
approved