0,2

7*b(n)^2 - 5*a(n)^2 = 2 with companion sequence b(n)=A077417(n), n>=0.

a(n) = L(n,-12)*(-1)^n, where L is defined as in A108299; see also A077417 for L(n,+12). - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Jun 01 2005

Index entries for sequences related to linear recurrences with constant coefficients

Tanya Khovanova, Recursive Sequences

Index entries for sequences related to Chebyshev polynomials.

a(n) = 12*a(n-1) - a(n-2), a(-1)=-1, a(0)=1.

a(n) = S(n, 12) + S(n-1, 12) = S(2*n, sqrt(14)) with S(n, x) := U(n, x/2) Chebyshev's polynomials of the second kind. See A049310. S(-1, x)=0, S(n, 12)=A004191(n).

G.f.: (1+x)/(1-12*x+x^2).

a(n) = (ap^(2*n+1) - am^(2*n+1))/(ap - am) with ap := (sqrt(7)+sqrt(5))/sqrt(2) and am := (sqrt(7)-sqrt(5))/sqrt(2).

a(n)= sum(((-1)^k)*binomial(2*n-k, k)*14^(n-k), k=0..n).

a(n) = sqrt((7*A077417(n)^2 - 2)/5).

(Other) sage: [(lucas_number2(n, 12, 1)-lucas_number2(n-1, 12, 1))/10 for n in xrange(1, 18)]# [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Nov 10 2009]

Cf. A054320(n-1) with companion A072256(n), n>=1.

Sequence in context: A097168 A108366 A163415 this_sequence A102146 A097827 A142104

Adjacent sequences: A077413 A077414 A077415 this_sequence A077417 A077418 A077419

nonn,easy,new

Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), Nov 29 2002