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 A144720 a(0) = 2, a(1) = 3, a(n) = 4 * a(n-1) - a(n-2). 1
 2, 3, 10, 37, 138, 515, 1922, 7173, 26770, 99907, 372858, 1391525, 5193242, 19381443, 72332530, 269948677, 1007462178, 3759900035, 14032137962, 52368651813, 195442469290, 729401225347, 2722162432098, 10159248503045 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 LINKS Table of n, a(n) for n=0..23. Index entries for linear recurrences with constant coefficients, signature (4,-1). FORMULA Sequence satisfies -11 = f(a(n), a(n+1)) where f(u, v) = u^2 + v^2 - 4*u*v. G.f.: (2 - 5*x) / (1 - 4*x + x^2). a(n) = (11 + a(n-1)^2) / a(n-2). MATHEMATICA LinearRecurrence[{4, -1}, {2, 3}, 30] (* Harvey P. Dale, Aug 29 2015 *) PROG (PARI) {a(n) = real( (2 + quadgen(12))^n * ( 2 - 1 / quadgen(12) ))} (PARI) {a(n) = subst( (4*polchebyshev(n) + polchebyshev(n-1)) / 3, x, 2)} CROSSREFS Cf. A144721(n) = a(-n). Sequence in context: A075890 A296269 A141102 * A164933 A003048 A008980 Adjacent sequences: A144717 A144718 A144719 * A144721 A144722 A144723 KEYWORD nonn AUTHOR Michael Somos, Sep 19 2008 STATUS approved

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Last modified May 21 15:23 EDT 2024. Contains 372738 sequences. (Running on oeis4.)