A126264 a(n) = 5*n^2 + 3*n.

8, 26, 54, 92, 140, 198, 266, 344, 432, 530, 638, 756, 884, 1022, 1170, 1328, 1496, 1674, 1862, 2060, 2268, 2486, 2714, 2952, 3200, 3458, 3726, 4004, 4292, 4590, 4898, 5216, 5544, 5882, 6230, 6588, 6956, 7334, 7722, 8120, 8528, 8946, 9374, 9812, 10260

Offset: 1

Author

Gary W. Adamson, Dec 22 2006

Keywords

• nonn
• easy

Examples

			a(24) = 5*24^2 + 3*24 = 2880 + 72 = 2952.
		

References

• L. B. W. Jolley, Summation of Series, Dover Publications, 1961, p. 12

Links

• G. C. Greubel, Table of n, a(n) for n = 1..5000
• Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Crossrefs

Cf. A001622, A147875.

Programs

Maple

a:=n->5*n^2+3*n: seq(a(n),n=1..55); # Emeric Deutsch, Apr 17 2007

Mathematica

Table[n*(5*n + 3), {n,1,50}] (* G. C. Greubel, Aug 23 2017 *)

PARI

a(n)=5*n^2+3*n \\ Charles R Greathouse IV, Jun 17 2017

Formula

Sum_{i=1..n} a(i) = n*(n+1)*(5n+7)/3 = 2*A162148(n).

a(n) = 2*A147875(n+1).

From G. C. Greubel, Aug 23 2017: (Start)

G.f.: 2*x*(x + 4)/(1 - x)^3.

E.g.f.: x*(5*x + 8)*exp(x). (End)

Sum_{n>=1} 1/a(n) = 5/9 + sqrt(1-2/sqrt(5))*Pi/6 + log(phi)*sqrt(5)/6 - 5*log(5)/12, where phi is the golden ratio (A001622). - Amiram Eldar, Aug 21 2022

Extensions

More terms from Emeric Deutsch, Apr 17 2007