A010004 a(0) = 1, a(n) = 13*n^2 + 2 for n>0.

1, 15, 54, 119, 210, 327, 470, 639, 834, 1055, 1302, 1575, 1874, 2199, 2550, 2927, 3330, 3759, 4214, 4695, 5202, 5735, 6294, 6879, 7490, 8127, 8790, 9479, 10194, 10935, 11702, 12495, 13314, 14159, 15030, 15927, 16850, 17799, 18774, 19775, 20802, 21855, 22934

Offset

0,2

Links

Bruno Berselli, Table of n, a(n) for n = 0..1000

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

Formula

G.f.: (1+x)*(1+11*x+x^2)/(1-x)^3. - Bruno Berselli, Feb 06 2012

E.g.f.: (x*(x+1)*13+2)*e^x-1. - Gopinath A. R., Feb 12 2012

Sum_{n>=0} 1/a(n) = 3/4+sqrt(26)/52*Pi*coth( Pi*sqrt(26)/13) = 1.1153332151579.. - R. J. Mathar, May 07 2024

Mathematica

Join[{1}, 13 Range[42]^2 + 2] (* Bruno Berselli, Feb 06 2012 *)
Join[{1}, LinearRecurrence[{3, -3, 1}, {15, 54, 119}, 50]] (* Vincenzo Librandi, Aug 03 2015 *)

Prog

(PARI) A010004(n)=13*n^2+2-!n   \\ M. F. Hasler, Feb 14 2012
(Magma) [1] cat [13*n^2+2: n in [1..50]]; // Vincenzo Librandi, Aug 03 2015

Crossrefs

Cf. A206399.

Sequence in context: A198955 A341563 A063436 * A172073 A059145 A086643

Adjacent sequences: A010001 A010002 A010003 * A010005 A010006 A010007

Keyword

nonn,easy

Author

N. J. A. Sloane.

Extensions

More terms from Bruno Berselli, Feb 06 2012

Status

approved