%I A077424
%S A077424 1,12,287,6876,164737,3946812,94558751,2265463212,54276558337,
%T A077424 1300371936876,31154649926687,746411226303612,17882714781360001,
%U A077424 428438743526336412,10264647129850713887,245923092372890796876
%N A077424 Chebyshev sequence T(n,12) with Diophantine property.
%C A077424 a(143+286k)-1 and a(143+286k)+1 are consecutive odd powerful numbers.
See A076445. - T. D. Noe (noe(AT)sspectra.com), May 04 2006
%H A077424 <a href="Sindx_Rea.html#recLCC">Index entries for sequences related to
linear recurrences with constant coefficients</a>
%H A077424 Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/
RecursiveSequences.html">Recursive Sequences</a>
%H A077424 <a href="Sindx_Ch.html#Cheby">Index entries for sequences related to
Chebyshev polynomials.</a>
%F A077424 a(n+1)^2 - 143*b(n)^2 = 1, n>=0, with the companion sequence b(n)=A077423(n).
%F A077424 a(n)=24*a(n-1) - a(n-2), a(-1) := 12, a(0)=1.
%F A077424 a(n)= T(n, 12)= (S(n, 24)-S(n-2, 24))/2 = S(n, 24)-11*S(n-1, 24) with
T(n, x), resp. S(n, x), Chebyshev's polynomials of the first, resp.
second, kind. See A053120 and A049310. S(n, 24)=A077423(n).
%F A077424 a(n)= (ap^n + am^n)/2 with ap := 12+sqrt(143) and am := 12-sqrt(143).
%F A077424 a(n)= sum(((-1)^k)*(n/(2*(n-k)))*binomial(n-k, k)*(2*12)^(n-2*k), k=0..floor(n/
2)), n>=1.
%F A077424 a(n+1)=sqrt(1 + 143*A077423(n)^2), n>=0.
%F A077424 G.f.: (1-12*x)/(1-24*x+x^2).
%o A077424 sage: [lucas_number2(n,24,1)/2 for n in xrange(0,20)] - Zerinvary Lajos
(zerinvarylajos(AT)yahoo.com), Jun 26 2008
%Y A077424 Cf. A090732.
%Y A077424 Sequence in context: A009604 A154669 A079519 this_sequence A159827 A145448
A001164
%Y A077424 Adjacent sequences: A077421 A077422 A077423 this_sequence A077425 A077426
A077427
%K A077424 nonn,easy
%O A077424 0,2
%A A077424 Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), Nov 29
2002
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