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A144720
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a(0) = 2, a(1) = 3, a(n) = 4 * a(n-1) - a(n-2).
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1
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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; internal format)
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OFFSET
| 0,1
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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).
a(n)=(1/6)*sqrt(3)*[2-sqrt(3)]^n-(1/6)*sqrt(3)*[2+sqrt(3)]^n+[2-sqrt(3)]^n+[2+sqrt(3)]^n, with n>=0 [From Paolo P. Lava (paoloplava(AT)gmail.com), Oct 15 2008]
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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)}
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CROSSREFS
| Cf. A144721(n) = a(-n).
Sequence in context: A056607 A060604 A141102 * A164933 A003048 A008980
Adjacent sequences: A144717 A144718 A144719 * A144721 A144722 A144723
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KEYWORD
| nonn
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AUTHOR
| Michael Somos, Sep 19 2008
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