A010020 a(0) = 1, a(n) = 31*n^2 + 2 for n>0.

1, 33, 126, 281, 498, 777, 1118, 1521, 1986, 2513, 3102, 3753, 4466, 5241, 6078, 6977, 7938, 8961, 10046, 11193, 12402, 13673, 15006, 16401, 17858, 19377, 20958, 22601, 24306, 26073, 27902, 29793, 31746, 33761, 35838, 37977, 40178, 42441, 44766, 47153, 49602

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

Mathematica

Join[{1}, 31 Range[40]^2 + 2] (* Bruno Berselli, Feb 07 2012 *)
Join[{1}, LinearRecurrence[{3, -3, 1}, {33, 126, 281}, 50]] (* Vincenzo Librandi, Aug 03 2015 *)

Formula

G.f.: (1+x)*(1+29*x+x^2)/(1-x)^3. - Bruno Berselli, Feb 07 2012

E.g.f.: (x*(x+1)*31+2)*e^x-1. - Gopinath A. R., Feb 14 2012

Sum_{n>=0} 1/a(n) = 3/4 + sqrt(62)/124 *Pi*coth(Pi*sqrt(62)/31) = 1.05093832062... - R. J. Mathar, May 07 2024