A239794 5*n^2 + 4*n - 15.

-6, 13, 42, 81, 130, 189, 258, 337, 426, 525, 634, 753, 882, 1021, 1170, 1329, 1498, 1677, 1866, 2065, 2274, 2493, 2722, 2961, 3210, 3469, 3738, 4017, 4306, 4605, 4914, 5233, 5562, 5901, 6250, 6609, 6978, 7357, 7746, 8145, 8554, 8973, 9402, 9841, 10290

Offset

1,1

Comments

Follows the integer values from 1 on the quadratic equation 5*x^2 + 4*n - 15, this is the case x=n.

Links

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

WolframAlpha, Table of 5n^2+4n-15

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

Formula

From Bruno Berselli, Mar 27 2014: (Start)

G.f.: -x*(6 - 31*x + 15*x^2)/(1 - x)^3.

a(n+1) - a(n) = A017377(n).

a(n) - a(-n) = A008590(n). (End)

Example

For n=3, a(3) = 5*3^2 + 4*3 - 15 = 42; for n=6, a(6) = 5*6^2 + 4*6 - 15 = 189.

Mathematica

Table[5 n^2 + 4 n - 15, {n, 50}]
CoefficientList[Series[(6 - 31 x + 15 x^2)/(x - 1)^3, {x, 0, 50}], x] (* Vincenzo Librandi, Mar 29 2014 *)

Prog

(Magma) [5*n^2+4*n-15: n in [1..50]];
(PARI) a(n)=5*n^2+4*n-15 \\ Charles R Greathouse IV, Jun 17 2017

Crossrefs

Cf. A008590, A017377.

Sequence in context: A338267 A216508 A057451 * A034753 A100905 A353964

Adjacent sequences: A239791 A239792 A239793 * A239795 A239796 A239797

Keyword

sign,easy

Author

Katherine Guo, Mar 26 2014

Status

approved