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A047235
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Numbers that are congruent to {2, 4} mod 6.
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14
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2, 4, 8, 10, 14, 16, 20, 22, 26, 28, 32, 34, 38, 40, 44, 46, 50, 52, 56, 58, 62, 64, 68, 70, 74, 76, 80, 82, 86, 88, 92, 94, 98, 100, 104, 106, 110, 112, 116, 118, 122, 124, 128, 130, 134, 136, 140, 142, 146, 148, 152, 154, 158, 160, 164, 166, 170, 172, 176, 178, 182, 184, 188, 190, 194, 196, 200, 202, 206
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| Apart from initial term(s), dimension of the space of weight 2n cuspidal newforms for Gamma_0( 19 ).
Complement of A047273; A093719(a(n)) = 0. [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Oct 01 2008]
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LINKS
| C. Lai, A note on potentially K_4-e graphical sequences
William A. Stein, Dimensions of the spaces S_k^{new}(Gamma_0(N))
William A. Stein, The modular forms database
Index to sequences with linear recurrences with constant coefficients, signature (1,1,-1).
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FORMULA
| n such that phi(3n)=phi(2n) - Benoit Cloitre (benoit7848c(AT)orange.fr), Aug 06 2003
G.f.: 2x(1+x+x^2)/((1+x)(1-x)^2). a(n) = 3n -3/2 -(-1)^n/2. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Nov 22 2008]
a(n) = 3n+5..n odd, 3n+4..n even a(n) = 6*floor((n+1)/2) +3 + (-1)^n [From Gary Detlefs (gdetlefs(AT)aol.com), Mar 02 2010]
a(n)=6*n-a(n-1)-6 (with a(1)=2) [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Aug 05 2010]
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EXAMPLE
| For n=2, a(2)=6*2-2-6=4; n=3, a(3)=6*3-4-6=8; n=4, a(4)=6*4-8-6=10 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Aug 05 2010]
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MAPLE
| seq(6*floor((n+1)/2) +3 + (-1)^n, n= 1..67); [From Gary Detlefs (gdetlefs(AT)aol.com), Mar 02 2010]
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PROG
| (MAGMA) [ n eq 1 select 2 else Self(n-1)+2*(1+n mod 2): n in [1..70] ]; [From Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Dec 13 2008]
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CROSSREFS
| Equals 2*A001651(n).
Cf. A007310 [(6*n+(-1)^n-3)/2]. [From Bruno Berselli (berselli.bruno(AT)yahoo.it), Jun 24 2010]
Sequence in context: A104197 A189792 A189782 * A087505 A086801 A154115
Adjacent sequences: A047232 A047233 A047234 * A047236 A047237 A047238
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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