A017581 a(n) = 12*n + 5.

5, 17, 29, 41, 53, 65, 77, 89, 101, 113, 125, 137, 149, 161, 173, 185, 197, 209, 221, 233, 245, 257, 269, 281, 293, 305, 317, 329, 341, 353, 365, 377, 389, 401, 413, 425, 437, 449, 461, 473, 485, 497, 509, 521, 533, 545, 557, 569, 581, 593, 605, 617, 629

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

Apart from initial term(s), dimension of the space of weight 2n cusp forms for Gamma_0(71).

A089911(2*a(n)) = 7. - Reinhard Zumkeller, Jul 05 2013

Equivalently, intersection of A016813 and A016789. - Bruno Berselli, Jan 24 2018

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..3000
• Tanya Khovanova, Recursive Sequences.
• William A. Stein, Dimensions of the spaces S_k(Gamma_0(N)).
• William A. Stein, The modular forms database.
• Index entries for linear recurrences with constant coefficients, signature (2,-1).

Crossrefs

Cf. A008594, A016789, A016813, A016969, A017533, A017545, A017593, A089911.

Programs

Haskell

a017581 = (+ 5) . (* 12)  -- Reinhard Zumkeller, Jul 05 2013

Magma

[12*n+5: n in [0..60]]; // Vincenzo Librandi, Jun 08 2011

Mathematica

12*Range[0,200]+5 (* Vladimir Joseph Stephan Orlovsky, Feb 19 2011 *)

PARI

a(n)=12*n+5 \\ Charles R Greathouse IV, Jul 10 2016

Formula

a(n) = 2*a(n-1) - a(n-2) for n>1, a(0)=5, a(1)=17. - Vincenzo Librandi, Jun 08 2011

G.f.: x*(5 + 7*x)/(1 - x)^2. - Wolfdieter Lang, Jul 04 2023

E.g.f.: exp(x)*(5 + 12*x). - Stefano Spezia, Feb 21 2024

a(n) = A016969(2*n) = A016789(4*n+1). - Elmo R. Oliveira, Apr 10 2025