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A046727
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Related to Pythagorean triples: alternate terms of A001652 and A046090.
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4
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0, 3, 21, 119, 697, 4059, 23661, 137903, 803761, 4684659, 27304197, 159140519, 927538921, 5406093003, 31509019101, 183648021599, 1070379110497, 6238626641379, 36361380737781, 211929657785303, 1235216565974041
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| For a triple (a,b,c) there exist k,m such that (a,b,c) = (k^2-m^2, 2km, k^2+m^2). Here k = A001333(n) and m = A001333(n+1), so this sequence is identical to the Pell oblongs A084159 for n>0. - Lambert Klasen (Lambert.Klasen(AT)gmx.de), Nov 10 2004
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REFERENCES
| A. H. Beiler, Recreations in the Theory of Numbers. New York: Dover, pp. 122-125, 1964.
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LINKS
| Reinhard Zumkeller, Table of n, a(n) for n = 0..1000
A. Bogomolny, The Trinary Tree(s) underlying Primitive Pythagorean Triples.
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FORMULA
| Values of x obtained by repeatedly multiplying the triple (x, y, z)=(3, 4, 5) by the matrix A = ([1 2 2] [2 1 2] [2 2 3]), the Across matrix of "The Trinary Tree(s) underlying Primitive Pythagorean Triples" generating matrices. - Vim Wenders (vim(AT)gmx.li), Jan 14 2004
For n>0 a(n)=A001333(n)*A001333(n+1) - Lambert Klasen (Lambert.Klasen(AT)gmx.de), Nov 10 2004
G.f.: x*(3+6*x-x^2)/((1+x)*(1-6*x+x^2)). [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jul 08 2009]
a(n)+a(n+1)=A005319(n+1), n>0. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jul 13 2009]
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PROG
| (Haskell)
a046727 n = a046727_list !! n
a046727_list = 0 : f (tail a001652_list) (tail a046090_list) where
f (x:_:xs) (_:y:ys) = x : y : f xs ys
-- Reinhard Zumkeller, 10 Jan 2012
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CROSSREFS
| Cf. A046729. Essentially the same as A084159.
Sequence in context: A092634 A178537 * A084159 A117512 A068127 A171137
Adjacent sequences: A046724 A046725 A046726 * A046728 A046729 A046730
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KEYWORD
| easy,nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| More terms from Sascha Kurz (sascha.kurz(AT)uni-bayreuth.de), Jan 23 2003
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