%I A077236
%S A077236 4,11,40,149,556,2075,7744,28901,107860,402539,1502296,5606645,
%T A077236 20924284,78090491,291437680,1087660229,4059203236,15149152715,
%U A077236 56537407624,211000477781,787464503500,2938857536219,10967965641376
%N A077236 Bisection (even part) of Chebyshev sequence with Diophantine property.
%C A077236 a(n)^2 - 3*b(n)^2 = 13, with the companion sequence b(n)= A054491(n).
%C A077236 The odd part is A077235(n) with Diophantine companion A077234(n).
%H A077236 <a href="Sindx_Rea.html#recLCC">Index entries for sequences related to 
               linear recurrences with constant coefficients</a>
%H A077236 Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/
               RecursiveSequences.html">Recursive Sequences</a>
%H A077236 <a href="Sindx_Ch.html#Cheby">Index entries for sequences related to 
               Chebyshev polynomials.</a>
%F A077236 a(n)= T(n+1, 2)+2*T(n, 2), with T(n, x) Chebyshev's polynomials of the 
               first kind, A053120. T(n, 2)= A001075(n).
%F A077236 G.f.: (4-5*x)/(1-4*x+x^2).
%F A077236 a(n)=4*a(n-1)-a(n-2) with a(0)=4 and a(1)=11. [From Philippe DELEHAM 
               (kolotoko(AT)wanadoo.fr), Nov 16 2008]
%F A077236 a(n)=-(1/2)*sqrt(3)*[2-sqrt(3)]^n+(1/2)*sqrt(3)*[2+sqrt(3)]^n+2*[2-sqrt(3)]^n+2*[2 
               +sqrt(3)]^n, with n>=0 [From Paolo P. Lava (ppl(AT)spl.at), Nov 20 
               2008]
%F A077236 a(n)=((4+sqrt3)(2+sqrt3)^n+(4-sqrt3)(2-sqrt3)^n)/2. Offset 0. a(n)=second 
               binomial transform of 4,3,12,9,36. [From Al Hakanson (hawkuu(AT)gmail.com), 
               Jul 06 2009]
%e A077236 11 = a(1) = sqrt(3*A054491(1)^2 + 13) = sqrt(3*6^2 + 13)= sqrt(121) = 
               11.
%Y A077236 Cf. A077238 (even and odd parts).
%Y A077236 Sequence in context: A149266 A149267 A149268 this_sequence A152532 A121096 
               A047091
%Y A077236 Adjacent sequences: A077233 A077234 A077235 this_sequence A077237 A077238 
               A077239
%K A077236 nonn,easy
%O A077236 0,1
%A A077236 Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), Nov 08, 
               2002