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 A077246 Bisection (even part) of Chebyshev sequence with Diophantine property. 4
 2, 13, 102, 803, 6322, 49773, 391862, 3085123, 24289122, 191227853, 1505533702, 11853041763, 93318800402, 734697361453, 5784260091222, 45539383368323, 358530806855362, 2822707071474573, 22223125764941222 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS 3*a(n)^2 - 5*b(n)^2 = 7, with the companion sequence b(n)= A077245(n). The odd part is A077244(n) with Diophantine companion A077243(n). LINKS Tanya Khovanova, Recursive Sequences Index entries for linear recurrences with constant coefficients, signature (8,-1). FORMULA a(n)= 8*a(n-1) - a(n-2), a(-1) := 3, a(0)=2. a(n)= (T(n+1, 4)+2*T(n, 4))/3, with T(n, x) Chebyshev's polynomials of the first kind, A053120. T(n, 4)= A001091(n). G.f.: (2-3*x)/(1-8*x+x^2). a(n)=[4-sqrt(15)]^n-(1/6)*[4-sqrt(15)]^n*sqrt(15)+[4+sqrt(15)]^n+(1/6)*sqrt(15)*[4 +sqrt(15)]^n, with n>=0 - Paolo P. Lava, Jul 08 2008 EXAMPLE 13 = a(1) = sqrt((5*A077245(1)^2 + 7)/3) = sqrt((5*10^2 + 7)/3) = sqrt(169) = 13. MATHEMATICA LinearRecurrence[{8, -1}, {2, 13}, 30] (* Harvey P. Dale, Apr 30 2012 *) CROSSREFS Sequence in context: A141116 A234299 A301355 * A266906 A107000 A046891 Adjacent sequences:  A077243 A077244 A077245 * A077247 A077248 A077249 KEYWORD nonn,easy AUTHOR Wolfdieter Lang, Nov 08 2002 STATUS approved

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Last modified October 21 03:24 EDT 2019. Contains 328291 sequences. (Running on oeis4.)