A010003 a(0) = 1, a(n) = 11*n^2 + 2 for n>0.

1, 13, 46, 101, 178, 277, 398, 541, 706, 893, 1102, 1333, 1586, 1861, 2158, 2477, 2818, 3181, 3566, 3973, 4402, 4853, 5326, 5821, 6338, 6877, 7438, 8021, 8626, 9253, 9902, 10573, 11266, 11981, 12718, 13477, 14258, 15061, 15886, 16733, 17602, 18493, 19406

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

Apart from the first term, numbers of the form (r^2+2*s^2)*n^2+2 = (r*n)^2+(s*n-1)^2+(s*n+1)^2: in this case is r=3, s=1. After 13, all terms are in A000408. - Bruno Berselli, Feb 06 2012

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

Mathematica

Join[{1}, 11 Range[41]^2 + 2] (* Bruno Berselli, Feb 06 2012 *)
Join[{1}, LinearRecurrence[{3, -3, 1}, {13, 46, 101}, 50]] (* Vincenzo Librandi, Aug 03 2015 *)

PARI

A010003(n)=11*n^2+2-!n   \\ M. F. Hasler, Feb 14 2012

Formula

G.f.: (1+x)*(1+9*x+x^2)/(1-x)^3. - Bruno Berselli, Feb 06 2012

E.g.f.: (x*(x+1)*11+2)*e^x-1. - Gopinath A. R., Feb 14 2012

Sum_{n>=0} 1/a(n) = 3/4+sqrt(22)/44*Pi*coth( Pi*sqrt(22)/11) = 1.134242719070... - R. J. Mathar, May 07 2024

Extensions

More terms from Bruno Berselli, Feb 06 2012