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Search: id:A078370
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| 5, 13, 29, 53, 85, 125, 173, 229, 293, 365, 445, 533, 629, 733, 845, 965, 1093, 1229, 1373, 1525, 1685, 1853, 2029, 2213, 2405, 2605, 2813, 3029, 3253, 3485, 3725, 3973, 4229, 4493, 4765, 5045, 5333
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OFFSET
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0,1
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COMMENT
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This is the generic form of D in the (nontrivially) solvable Pell equation x^2 - D*y^2 = -4. See A078356-7.
1/5 + 1/13 + 1/29 +...= (Pi/8)*tanh Pi [Jolley] - Gary W. Adamson (qntmpkt(AT)yahoo.com), Dec 21 2006
Except for the first term, a(n)=8*n+a(n-1), (with a(1)=13) [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Oct 24 2009]
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REFERENCES
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L. B. W. Jolley, "Summation of Series", Dover Publications, 1961, p. 176.
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LINKS
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Index entries for sequences related to linear recurrences with constant coefficients
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FORMULA
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a(n)=4*(n+1)*n =8*binomial(n+1, 2)+5, hence subsequence of A004770 (5 (mod 8) numbers).
G.f.: (5-2*x+5*x^2)/(1-x)^3.
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CROSSREFS
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Subsequence of A077426 (D values (not a square) for which Pell x^2 - D*y^2 = -4 is solvable in positive integers).
Sequence in context: A129371 A130230 A106931 this_sequence A005473 A086732 A162329
Adjacent sequences: A078367 A078368 A078369 this_sequence A078371 A078372 A078373
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KEYWORD
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nonn,easy
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AUTHOR
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Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), Nov 29 2002
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