A010011 a(0) = 1, a(n) = 21*n^2 + 2 for n>0.

1, 23, 86, 191, 338, 527, 758, 1031, 1346, 1703, 2102, 2543, 3026, 3551, 4118, 4727, 5378, 6071, 6806, 7583, 8402, 9263, 10166, 11111, 12098, 13127, 14198, 15311, 16466, 17663, 18902, 20183, 21506, 22871, 24278, 25727, 27218, 28751, 30326, 31943, 33602, 35303

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

Magma

[1] cat [21*n^2+2: n in [1..50]]; // Vincenzo Librandi, Aug 03 2015

Maple

A010011:=n->`if`(n=0,1,21*n^2+2); seq(A010011(n), n=0..100); # Wesley Ivan Hurt, Nov 15 2013

Mathematica

Join[{1}, 21 Range[41]^2 + 2] (* Bruno Berselli, Feb 06 2012 *)
Join[{1}, LinearRecurrence[{3, -3, 1}, {23, 86, 191}, 50]] (* Vincenzo Librandi, Aug 03 2015 *)

Formula

O.g.f.: 1-x*(23+17*x+2*x^2)/(-1+x)^3. - R. J. Mathar, Apr 12 2008

E.g.f.: (21*x*(x+1)+2)*e^x-1. - Gopinath A. R., Feb 13 2012

Sum_{n>=0} 1/a(n) = 3/4+sqrt(42)/84*Pi*coth( Pi*sqrt(42)/21) = 1.0738233857899... - R. J. Mathar, May 07 2024

a(n) = A069178(n)+A069178(n+1). - R. J. Mathar, May 07 2024