A156376 a(n) = 30*n + 19.

19, 49, 79, 109, 139, 169, 199, 229, 259, 289, 319, 349, 379, 409, 439, 469, 499, 529, 559, 589, 619, 649, 679, 709, 739, 769, 799, 829, 859, 889, 919, 949, 979, 1009, 1039, 1069, 1099, 1129, 1159, 1189, 1219, 1249, 1279, 1309, 1339, 1369, 1399, 1429, 1459, 1489

Offset: 0

Author

Vincenzo Librandi, Aug 12 2009

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (2,-1).

Programs

Magma

I:=[19, 49]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..50]]; // Vincenzo Librandi, Mar 01 2012

Mathematica

Range[19, 7000, 30] (* Vladimir Joseph Stephan Orlovsky, Jul 13 2011 *)
LinearRecurrence[{2, -1}, {19, 49}, 50] (* Vincenzo Librandi, Mar 01 2012 *)

Formula

a(n) = 2*a(n-1) - a(n-2).

G.f.: (19+11*x)/(x-1)^2.

Sum_{n>=0} a(n)/(16*(n+1)^3*(2*n+1)*binomial(2*n+1,n)^2) = zeta(3). - Daniel Suteu, Oct 31 2017

E.g.f.: exp(x)*(19 + 30*x). - Elmo R. Oliveira, Dec 08 2024

Extensions

Offset corrected by R. J. Mathar, Oct 12 2009