Search: id:A003185
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%I A003185
%S A003185 5,45,117,221,357,525,725,957,1221,1517,1845,2205,2597,
%T A003185 3021,3477,3965,4485,5037,5621,6237,6885,7565,8277,9021,
%U A003185 9797,10605,11445,12317,13221,14157,15125,16125,17157,18221
%N A003185 (4n+1)(4n+5).
%C A003185 Bisection of A078371. - Lambert Klasen (Lambert.Klasen(AT)gmx.net), Nov 
               19 2004
%F A003185 1 = Sum(0 through infinity): 4/a(n). Sum(k = 0 through n) 4/a(k) = 4(n+1)/
               [4(n+1)+1] Definite integral(0 to 1) 1/(1 + x^4) = Sum(0 through 
               infinity) 4/a(2n) = Sum(0 through infinity) (-1)^n/(4n+1) - Gary 
               W. Adamson (qntmpkt(AT)yahoo.com), Jun 18 2003
%F A003185 1 = 1/5 + Sum(n=1, inf, 16/a(n)); with partial sums (4n+1)/(4n+5). - 
               Gary W. Adamson (qntmpkt(AT)yahoo.com), Jun 18 2003
%F A003185 O.g.f.: (-5-30*x+3*x^2)/(-1+x)^3. a(3n)=A001513(2n). Conjecture: a(n+1)-a(n)=A063164(n+2). 
               - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Apr 04 2008
%o A003185 (PARI) for(n=0,80,print1((4*n+3)*(4*n+7),", "))
%Y A003185 Cf. A078371, A003185.
%Y A003185 Sequence in context: A058792 A113948 A096763 this_sequence A027801 A079139 
               A081070
%Y A003185 Adjacent sequences: A003182 A003183 A003184 this_sequence A003186 A003187 
               A003188
%K A003185 nonn
%O A003185 0,1
%A A003185 N. J. A. Sloane (njas(AT)research.att.com).

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