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FORMULA
| a(n+1)^2 - 30*(2*b(n))^2 = 1, n>=0, with the companion sequence b(n)=A077421(n).
a(n)=22*a(n-1) - a(n-2), a(-1) := 11, a(0)=1.
a(n)= T(n, 11)= (S(n, 22)-S(n-2, 22))/2 = S(n, 22)-11*S(n-1, 22) with T(n, x), resp. S(n, x), Chebyshev's polynomials of the first, resp. second, kind. See A053120 and A049310. S(n, 22)=A077421(n).
a(n)= (ap^n + am^n)/2 with ap := 11+2*sqrt(30) and am := 11-2*sqrt(30).
a(n)= sum(((-1)^k)*(n/(2*(n-k)))*binomial(n-k, k)*(2*11)^(n-2*k), k=0..floor(n/2)), n>=1.
a(n+1)=sqrt(1 + 30*(2*A077421(n))^2), n>=0.
a(n) = Cosh[2n*ArcSinh[Sqrt[5]]] - Herbert Kociemba (kociemba(AT)t-online.de), Apr 24 2008
G.f.: (1-11*x)/(1-22*x+x^2). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 17 2008]
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PROG
| sage: [lucas_number2(n, 22, 1)/2 for n in xrange(0, 20)] - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 26 2008
(MAGMA) [n: n in [1..10000000] |IsSquare(30*(n^2-1))] [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Aug 08 2010]
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