

A017593


a(n) = 12*n + 6.


18



6, 18, 30, 42, 54, 66, 78, 90, 102, 114, 126, 138, 150, 162, 174, 186, 198, 210, 222, 234, 246, 258, 270, 282, 294, 306, 318, 330, 342, 354, 366, 378, 390, 402, 414, 426, 438, 450, 462, 474, 486, 498, 510, 522, 534, 546, 558, 570, 582, 594, 606, 618, 630, 642
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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 mth 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

Table of n, a(n) for n=0..53.
P. Fortuny, J. M. Grau, A. M. OllerMarcén, I. F. Rúa, On power sums of matrices over a finite commutative ring, arXiv:1505.08132 [math.RA], 2015.
M. Janjic and B. Petkovic, A Counting Function, arXiv 1301.4550 [math.CO], 2013.
Luis Manuel Rivera, Integer sequences and kcommuting permutations, arXiv preprint arXiv:1406.3081 [math.CO], 20142015.
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(n1) with n > 0, a(0)=6.  Vincenzo Librandi, Nov 19 2010
a(0)=6, a(1)=18; for n > 1, a(n) = 2*a(n1)  a(n2).  Harvey P. Dale, Aug 20 2014
G.f.: 6*(1+x)/(1x)^2.  Wolfdieter Lang, Oct 27 2020


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

Cf. A017641.
Sequence in context: A304050 A242394 A030568 * A335908 A096286 A256256
Adjacent sequences: A017590 A017591 A017592 * A017594 A017595 A017596


KEYWORD

nonn,easy


AUTHOR

N. J. A. Sloane


EXTENSIONS

Typos in sequence (270 was 2,70 and 510 was 5,10) fixed by Peter Luschny, Dec 14 2009


STATUS

approved



