OFFSET
0,1
COMMENTS
Apart from initial term(s), dimension of the space of weight 2n cuspidal newforms for Gamma_0(73).
Continued fraction expansion of tanh(1/6). - Benoit Cloitre, Dec 17 2002
Also solutions to 5^x + 7^x == 11 (mod 13). - Cino Hilliard, May 10 2003
Numbers m such that the sum of the m-th powers of all 2 X 2 matrices over Z/mZ is a nonzero matrix. - José María Grau Ribas, Jan 31 2014
Positive numbers k for which 1/2 + k/4 + k^2/6 is an integer. - Bruno Berselli, Apr 12 2018
LINKS
P. Fortuny, J. M. Grau, A. M. Oller-Marcén and I. F. Rúa, On power sums of matrices over a finite commutative ring, arXiv:1505.08132 [math.RA], 2015.
Milan Janjic and Boris Petkovic, A Counting Function, arXiv 1301.4550 [math.CO], 2013.
Luis Manuel Rivera, Integer sequences and k-commuting permutations, arXiv preprint arXiv:1406.3081 [math.CO], 2014-2015.
William A. Stein, Dimensions of the spaces S_k^{new}(Gamma_0(N)).
William A. Stein, The modular forms database.
Index entries for linear recurrences with constant coefficients, signature (2,-1).
FORMULA
A030133(a(n)) = 9. - Reinhard Zumkeller, Jul 04 2007
a(n) = 24*n - a(n-1) with n > 0, a(0)=6. - Vincenzo Librandi, Nov 19 2010
a(0)=6, a(1)=18; for n > 1, a(n) = 2*a(n-1) - a(n-2). - Harvey P. Dale, Aug 20 2014
G.f.: 6*(1+x)/(1-x)^2. - Wolfdieter Lang, Oct 27 2020
Sum_{n>=0} (-1)^n/a(n) = Pi/24 (A019691). - Amiram Eldar, Dec 12 2021
From Amiram Eldar, Nov 24 2024: (Start)
Product_{n>=0} (1 - (-1)^n/a(n)) = sqrt(2) * sin(5*Pi/24).
Product_{n>=0} (1 + (-1)^n/a(n)) = sqrt(2) * cos(5*Pi/24). (End)
MATHEMATICA
12 Range[0, 200] + 6 (* Vladimir Joseph Stephan Orlovsky, Feb 19 2011 *)
LinearRecurrence[{2, -1}, {6, 18}, 60] (* Harvey P. Dale, Aug 20 2014 *)
PROG
(Sage) [i+6 for i in range(645) if gcd(i, 12) == 12] # Zerinvary Lajos, May 21 2009
(PARI) a(n)=12*n+6 \\ Charles R Greathouse IV, Sep 24 2015
CROSSREFS
KEYWORD
nonn,easy,changed
AUTHOR
EXTENSIONS
Typos in sequence (270 was 2,70 and 510 was 5,10) fixed by Peter Luschny, Dec 14 2009
STATUS
approved