1,3

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)

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

Also numbers n such that Kronecker(4,n)==mu(gcd(4,n)). - Jon Perry (perry(AT)globalnet.co.uk), Sep 17 2002

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

For n>1, equals union of A020883 and A020884. - Lekraj Beedassy (blekraj(AT)yahoo.com), Sep 28 2004

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

Index entries for sequences related to linear recurrences with constant coefficients

Ron Knott, Pythagorean Triples and Online Calculators

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.

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

(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)))))

Cf. A047209, A020883 and A020884.

Sequence in context: A137905 A074227 A122906 this_sequence A005848 A039065 A139711

Adjacent sequences: A042962 A042963 A042964 this_sequence A042966 A042967 A042968

nonn,nice

N. J. A. Sloane (njas(AT)research.att.com).

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