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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| 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 ).
n such that n and (n+1) have the same binary digital sum - Benoit Cloitre (benoit7848c(AT)orange.fr), Jun 05 2002
A056753(a(n)) = 3. [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Aug 23 2009]
A179821(a(n)) = a(A179821(n)). [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Jul 31 2010]
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REFERENCES
| Konrad Knopp, Theory and Application of Infinite Series, Dover, p. 269
L. B. W. Jolley, "Summation of Series", Dover Publications, 1961, p. 16.
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LINKS
| Index entries for sequences related to linear recurrences with constant coefficients
Tanya Khovanova, Recursive Sequences
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
Konrad Knopp, Theorie und Anwendung der unendlichen Reihen, Berlin, J. Springer, 1922. (Original german edition of "Theory and Application of Infinite Series")
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FORMULA
| sum(n=1, inf, (-1)^n/a(n)) = 1/4/sqrt(2)*(Pi+2ln(sqrt(2)+1)) = A181048 [Jolley]. - Benoit Cloitre (benoit7848c(AT)orange.fr), Apr 05 2002
G.f.: (5-x)/(1-x)^2 - Paul Barry (pbarry(AT)wit.ie), Feb 27 2003
(1 + 5x + 9x^2 + 13x^3...) = (1 + 2x + 3x^2...) / (1 - 3x + 9x^2 -27x^3...) - Gary W. Adamson (qntmpkt(AT)yahoo.com), Jul 03 2003
a(n) = A001969(n) + A000069(n) . - DELEHAM Philippe (kolotoko(AT)wanadoo.fr), Feb 04 2004
a(n)=A004766(n-1). [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), 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 (kolotoko(AT)wanadoo.fr), Nov 03 2008]
a(n) = 8*n-2-a(n-1) (with a(0)=1). [From Vincenzo Librandi, Nov 20 2010]
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MATHEMATICA
| Range[1, 500, 4] (* From Vladimir Joseph Stephan Orlovsky (4vladimir(AT)gmail.com), May 26 2011 *)
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PROG
| (MAGMA) [ n: n in [1..250 by 4] ];
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CROSSREFS
| a(n)= A093561(n+1, 1), (4, 1)-Pascal column.
A161700, A005408, A016921, A017281, A017533, A158057, A161705, A161709, A161714, A128470. [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Jun 17 2009]
Sequence in context: A194395 A162502 A004766 * A198395 A190951 A057948
Adjacent sequences: A016810 A016811 A016812 * A016814 A016815 A016816
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KEYWORD
| nonn,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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