A010007 a(0) = 1, a(n) = 17*n^2 + 2 for n>0.

1, 19, 70, 155, 274, 427, 614, 835, 1090, 1379, 1702, 2059, 2450, 2875, 3334, 3827, 4354, 4915, 5510, 6139, 6802, 7499, 8230, 8995, 9794, 10627, 11494, 12395, 13330, 14299, 15302, 16339, 17410, 18515, 19654, 20827, 22034, 23275, 24550, 25859, 27202, 28579

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=2. After 1, 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 [17*n^2+2: n in [1..50]]; // Vincenzo Librandi, Aug 03 2015

Mathematica

Join[{1}, 17 Range[41]^2 + 2] (* Bruno Berselli, Feb 06 2012 *)
Join[{1}, LinearRecurrence[{3, -3, 1}, {19, 70, 155}, 50]] (* Vincenzo Librandi, Aug 03 2015 *)

Formula

G.f.: (1+x)*(1+15*x+x^2)/(1-x)^3. - Bruno Berselli, Feb 06 2012

E.g.f. : (x*(x+1)*17+2)*e^x-1. - Gopinath A. R., Feb 14 2012

Sum_{n>=0} 1/a(n) = 3/4+sqrt(34)/68*Pi*coth(Pi*sqrt(34)/17) = 1.09001290652... - R. J. Mathar, May 07 2024

a(n) = A069130(n)+A069130(n+1). - R. J. Mathar, May 07 2024

Extensions

More terms from Bruno Berselli, Feb 06 2012