A010022 a(0) = 1, a(n) = 40*n^2 + 2 for n>0.

1, 42, 162, 362, 642, 1002, 1442, 1962, 2562, 3242, 4002, 4842, 5762, 6762, 7842, 9002, 10242, 11562, 12962, 14442, 16002, 17642, 19362, 21162, 23042, 25002, 27042, 29162, 31362, 33642, 36002, 38442, 40962, 43562, 46242, 49002, 51842, 54762, 57762, 60842

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

First bisection of A005901. - Bruno Berselli, Feb 07 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 [40*n^2+2: n in [1..50]]; // Vincenzo Librandi, Aug 03 2015

Mathematica

Join[{1}, 40 Range[39]^2 + 2] (* Bruno Berselli, Feb 07 2012 *)
Join[{1}, LinearRecurrence[{3, -3, 1}, {42, 162, 362}, 50]] (* Vincenzo Librandi, Aug 03 2015 *)

Formula

G.f.: (1+x)*(1+38*x+x^2)/(1-x)^3; a(n) = A008253(4n). - Bruno Berselli, Feb 07 2012

E.g.f.: (x*(x+1)*40+2)*e^x-1. - Gopinath A. R., Feb 14 2012

Sum_{n>=0} 1/a(n) = 3/4 + sqrt(5)/40*Pi*coth(Pi*sqrt(5)/10) = 1.03983104279172.. - R. J. Mathar, May 07 2024

a(n) = 2*A158493(n), n>0. - R. J. Mathar, May 07 2024

a(n) = A195317(n)+A195317(n+1) = 2+10*A016742(n), n>0. - R. J. Mathar, May 07 2024