login
A239796
a(n) = 7*n^2 + 2*n - 15.
1
-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
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
KEYWORD
sign,easy
AUTHOR
Katherine Guo, Mar 26 2014
STATUS
approved