A010005 a(0) = 1, a(n) = 15*n^2 + 2 for n>0.

1, 17, 62, 137, 242, 377, 542, 737, 962, 1217, 1502, 1817, 2162, 2537, 2942, 3377, 3842, 4337, 4862, 5417, 6002, 6617, 7262, 7937, 8642, 9377, 10142, 10937, 11762, 12617, 13502, 14417, 15362, 16337, 17342, 18377, 19442, 20537, 21662, 22817, 24002, 25217, 26462

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

• Bruno Berselli, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Crossrefs

Cf. A206399.

Programs

Magma

[1] cat [15*n^2+2: n in [1..50]]; // Vincenzo Librandi, Aug 03 2015

Mathematica

Join[{1}, 15 Range[42]^2 + 2] (* Bruno Berselli, Feb 06 2012 *)
Join[{1}, LinearRecurrence[{3, -3, 1}, {17, 62, 137}, 50]] (* Vincenzo Librandi, Aug 03 2015 *)

PARI

A010005(n)=15*n^2+2-!n   \\ M. F. Hasler, Feb 14 2012

Formula

G.f.: (1+x)*(1+13*x+x^2)/(1-x)^3. - Bruno Berselli, Feb 06 2012

E.g.f.: (x*(x+1)*15+2)*e^x-1. - Gopinath A. R., Feb 14 2012

Sum_{n>=0} 1/a(n) = 3/4+sqrt(30)/60*Pi*coth(Pi *sqrt(30)/15) = 1.101107302494... - R. J. Mathar, May 07 2024

Extensions

More terms from Bruno Berselli, Feb 06 2012