A010013 a(0) = 1, a(n) = 23*n^2 + 2 for n>0.

1, 25, 94, 209, 370, 577, 830, 1129, 1474, 1865, 2302, 2785, 3314, 3889, 4510, 5177, 5890, 6649, 7454, 8305, 9202, 10145, 11134, 12169, 13250, 14377, 15550, 16769, 18034, 19345, 20702, 22105, 23554, 25049, 26590, 28177, 29810, 31489, 33214, 34985, 36802, 38665

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

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

Mathematica

Join[{1}, 23 Range[41]^2 + 2] (* Bruno Berselli, Feb 06 2012 *)

Formula

G.f.: (1+x)*(1+21*x+x^2)/(1-x)^3. - Bruno Berselli, Feb 06 2012

E.g.f.: (x*(x+1)*23+2)*e^x-1. - Gopinath A. R., Feb 14 2012

Sum_{n>=0} 1/a(n) = 3/4 + sqrt(46)/92*Pi*coth( Pi*sqrt(46)/23) = 1.0677349581... - R. J. Mathar, May 07 2024

a(n) = A069174(n)+A069174(n+1). - R. J. Mathar, May 07 2024