Search: id:A042965
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%I A042965
%S A042965 0,1,3,4,5,7,8,9,11,12,13,15,16,17,19,20,21,23,24,25,27,28,29,31,32,33,
%T A042965 35,36,37,39,40,41,43,44,45,47,48,49,51,52,53,55,56,57,59,60,61,63,
%U A042965 64,65,67,68,69,71,72,73,75,76,77,79,80,81,83,84,85,87,88,89,91,92
%N A042965 Numbers not congruent to 2 mod 4.
%C A042965 Consider primitive Pythagorean triangles (A^2 + B^2 = C^2, (A, B) = 1, 
               A <= B); sequence (starting at 3) gives values of AUB, sorted and 
               duplicates removed. Values of AUBUC give same sequence - David W. 
               Wilson (davidwwilson(AT)comcast.net)
%C A042965 These are the nonnegative integers that can be written as a difference 
               of two squares i.e. n=x^2-y^2 for integers x,y. - Sharon Sela (sharonsela(AT)hotmail.com), 
               Jan 25 2002
%C A042965 Also numbers n such that Kronecker(4,n)==mu(gcd(4,n)). - Jon Perry (perry(AT)globalnet.co.uk), 
               Sep 17 2002
%C A042965 Count, sieving out numbers of the form 2(2n+1) (A016825, "nombres pair-impairs"). 
               A generalized Chebyshev transform of the Jacobsthal numbers: apply 
               the transform g(x)->(1/(1+x^2))g(x/(1+x^2)) to the g.f. of A001045(n+2). 
               Partial sums of 1,2,1,1,2,1,..... - Paul Barry (pbarry(AT)wit.ie), 
               Apr 26 2005
%C A042965 For n>1, equals union of A020883 and A020884. - Lekraj Beedassy (blekraj(AT)yahoo.com), 
               Sep 28 2004
%C A042965 The sequence 1,1,3,4,5,... is the image of A001045(n+1) under the mapping 
               g(x)->g(x/(1+x^2)). - Paul Barry (pbarry(AT)wit..ie), Jan 16 2005
%H A042965 <a href="Sindx_Rea.html#recLCC">Index entries for sequences related to 
               linear recurrences with constant coefficients</a>
%H A042965 Ron Knott, <a href="http://www.mcs.surrey.ac.uk/Personal/R.Knott/Pythag/
               pythag.html">Pythagorean Triples and Online Calculators</a>
%F A042965 Partial sums of the period-3 sequence 0, 1, 1, 2, 1, 1, 2, 1, 1, 2, ... 
               (A101825) with g.f. x*(1+x)^2/(1-x^3). - Ralf Stephan.
%F A042965 G.f. (follows from previous formula line): x(1+x)^2/(1-x-x^3+x^4); a(n)=sum{k=0..floor(n/
               2), binomial(n-k-1, k)A001045(n-2k)}, n>0. - Paul Barry (pbarry(AT)wit..ie), 
               Jan 16 2005
%o A042965 (PARI) for (x=1,200, for (y=1,200,if (kronecker(x,y)==moebius(gcd(x,y)),
               write("km.txt",x,";",y," : ",kronecker(x,y)))))
%Y A042965 Cf. A047209, A020883 and A020884.
%Y A042965 Sequence in context: A137905 A074227 A122906 this_sequence A005848 A039065 
               A139711
%Y A042965 Adjacent sequences: A042962 A042963 A042964 this_sequence A042966 A042967 
               A042968
%K A042965 nonn,nice
%O A042965 1,3
%A A042965 N. J. A. Sloane (njas(AT)research.att.com).
%E A042965 Edited by N. J. A. Sloane (njas(AT)research.att.com) at the suggestion 
               of Andrew Plewe, Peter Pein and Ralf Stephan, Jun 17 2007

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