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A017593 a(n) = 12*n + 6. 14
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 (list; graph; refs; listen; history; text; internal format)
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

Table of n, a(n) for n=0..53.

P. Fortuny, J. M. Grau, A. M. Oller-Marcén, 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 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

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 * A096286 A256256 A280802

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

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Last modified October 20 11:58 EDT 2018. Contains 316379 sequences. (Running on oeis4.)