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Search: id:A037213
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| A037213 |
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Expansion of sum(n*q^(n^2), n=0..inf). |
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+0
2
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| 0, 1, 0, 0, 2, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
(list; graph; listen)
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OFFSET
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0,5
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COMMENT
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Multiplicative with a(p^(2e)) = p^e, a(p^(2e+1)) = 0. Mitch Harris (Harris.Mitchell(AT)mgh.harvard.edu) Jun 09, 2005.
a(n) is the square root of n if n is square, zero otherwise [From Carl R. White (oeisfan(AT)phodd.net), May 23 2009]
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FORMULA
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Dirichlet generating function: zeta(2s-1). - Franklin T. Adams-Watters, Sep 11 2005.
a(n) = sqrt(n) * floor( cos^2(pi * sqrt(n)) ) [From Carl R. White (oeisfan(AT)phodd.net), May 23 2009]
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CROSSREFS
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Sequence in context: A036273 A112166 A112167 this_sequence A092197 A083804 A028597
Adjacent sequences: A037210 A037211 A037212 this_sequence A037214 A037215 A037216
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KEYWORD
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nonn,mult
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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