A010023 a(0) = 1, a(n) = 42*n^2 + 2 for n>0.

1, 44, 170, 380, 674, 1052, 1514, 2060, 2690, 3404, 4202, 5084, 6050, 7100, 8234, 9452, 10754, 12140, 13610, 15164, 16802, 18524, 20330, 22220, 24194, 26252, 28394, 30620, 32930, 35324, 37802, 40364, 43010, 45740, 48554, 51452, 54434, 57500, 60650, 63884

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

First bisection of A007899. - 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 [42*n^2+2: n in [1..50]]; // Vincenzo Librandi, Aug 03 2015

Mathematica

Join[{1}, 42 Range[39]^2 + 2] (* Bruno Berselli, Feb 07 2012 *)
Join[{1}, LinearRecurrence[{3, -3, 1}, {44, 170, 380}, 50]] (* Vincenzo Librandi, Aug 03 2015 *)

Formula

G.f.: (1+x)*(1+40*x+x^2)/(1-x)^3. - Bruno Berselli, Feb 07 2012

E.g.f.: (x*(x+1)*42+2)*e^x-1. - Gopinath A. R., Feb 14 2012

Sum_{n>=0} 1/a(n) = 3/4 + sqrt(21)/84*Pi*coth(Pi/sqrt(21)) = 1.0379904347... - R. J. Mathar, May 07 2024