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1, 5, 9, 13, 17, 21, 25, 29, 33, 37, 41, 45, 49, 53, 57, 61, 65, 69, 73, 77, 81, 85, 89, 93, 97, 101, 105, 109, 113, 117, 121, 125, 129, 133, 137, 141, 145, 149, 153, 157, 161, 165, 169, 173, 177, 181, 185, 189, 193, 197, 201, 205, 209, 213, 217, 221, 225, 229, 233, 237
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OFFSET
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0,2
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COMMENTS
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Apart from initial term(s), dimension of the space of weight 2n cusp forms for Gamma_0( 23 ).
Apart from initial term(s), dimension of the space of weight 2n cuspidal newforms for Gamma_0( 64 ).
Numbers n such that n and (n+1) have the same binary digital sum - Benoit Cloitre, Jun 05 2002
A056753(a(n)) = 3. [From Reinhard Zumkeller, Aug 23 2009]
A179821(a(n)) = a(A179821(n)). [From Reinhard Zumkeller, Jul 31 2010]
Numbers n such that (1 + sqrt(n))/2 is an algebraic integer. - Alonso del Arte, Jun 04 2012
Numbers n such that 2 is the only prime p that satisfies the relationship p XOR n = p + n. - Brad Clardy, Jul 22 2012
The identity (4*n+1)^2-(4*n^2+2*n)*(2)^2 = 1 can be written as a(n)^2 - A002943(n)*2^2 = 1. - Vincenzo Librandi, Mar 11 2009 - Nov 25 2012
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REFERENCES
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L. B. W. Jolley, "Summation of Series", Dover Publications, 1961, p. 16.
Konrad Knopp, Theory and Application of Infinite Series, Dover, p. 269
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for sequences related to linear recurrences with constant coefficients
Tanya Khovanova, Recursive Sequences
Konrad Knopp, Theorie und Anwendung der unendlichen Reihen, Berlin, J. Springer, 1922. (Original german edition of "Theory and Application of Infinite Series")
William A. Stein, Dimensions of the spaces S_k(Gamma_0(N))
William A. Stein, Dimensions of the spaces S_k^{new}(Gamma_0(N))
William A. Stein, The modular forms database
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FORMULA
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a(n) = A005408(2*n).
sum(n=1, inf, (-1)^n/a(n)) = 1/4/sqrt(2)*(Pi+2ln(sqrt(2)+1)) = A181048 [Jolley]. - Benoit Cloitre, Apr 05 2002
G.f.: (5-x)/(1-x)^2 - Paul Barry, Feb 27 2003
(1 + 5x + 9x^2 + 13x^3...) = (1 + 2x + 3x^2...) / (1 - 3x + 9x^2 -27x^3...) - Gary W. Adamson, Jul 03 2003
a(n) = A001969(n) + A000069(n) . - Philippe Deléham, Feb 04 2004
a(n) = A004766(n-1). [From R. J. Mathar, Oct 26 2008]
a(n) = 2*a(n-1)-a(n-2); a(0)=1, a(1)=5. a(n)=4+a(n-1). [From Philippe DELEHAM, Nov 03 2008]
a(n) = 8*n-2-a(n-1) (with a(0)=1). - Vincenzo Librandi, Nov 20 2010
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MATHEMATICA
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Range[1, 500, 4] (* From Vladimir Joseph Stephan Orlovsky, May 26 2011 *)
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PROG
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(MAGMA) [ n: n in [1..250 by 4] ];
(Haskell)
a016813 = (+ 1) . (* 4)
a016813_list = [1, 5 ..] -- Reinhard Zumkeller, Feb 14 2012
(PARI) a(n)=4*n+1 \\ Charles R Greathouse IV, Mar 22 2013
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CROSSREFS
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a(n)= A093561(n+1, 1), (4, 1)-Pascal column.
A161700, A016921, A017281, A017533, A158057, A161705, A161709, A161714, A128470. [From Reinhard Zumkeller, Jun 17 2009]
Subsequence of A042963.
Cf. A004772 (complement).
Sequence in context: A194395 A162502 A004766 * A198395 A190951 A057948
Adjacent sequences: A016810 A016811 A016812 * A016814 A016815 A016816
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane.
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STATUS
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approved
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