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A077238 Combined Diophantine Chebyshev sequences A077236 and A077235. 6

%I

%S 4,5,11,16,40,59,149,220,556,821,2075,3064,7744,11435,28901,42676,

%T 107860,159269,402539,594400,1502296,2218331,5606645,8278924,20924284,

%U 30897365,78090491,115310536,291437680,430344779,1087660229,1606068580,4059203236,5993929541

%N Combined Diophantine Chebyshev sequences A077236 and A077235.

%C a(n)^2 - 3*b(n)^2 = 13, with the companion sequence b(n)= A077237(n).

%C Positive values of x (or y) satisfying x^2 - 4xy + y^2 + 39 = 0. - _Colin Barker_, Feb 06 2014

%C Positive values of x (or y) satisfying x^2 - 14xy + y^2 + 624 = 0. - _Colin Barker_, Feb 16 2014

%H Vincenzo Librandi, <a href="/A077238/b077238.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Ch#Cheby">Index entries for sequences related to Chebyshev polynomials.</a>

%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (0,4,0,-1).

%F a(2*k)= A077236(k) and a(2*k+1)= A077235(k), k>=0.

%F G.f.: (1-x)*(4+9*x+4*x^2)/(1-4*x^2+x^4).

%F a(n) = 4*a(n-2)-a(n-4). - _Colin Barker_, Feb 06 2014

%e 11 = a(2) = sqrt(3*A077237(2)^2 + 13) = sqrt(3*6^2 + 13)= sqrt(121) = 11.

%t CoefficientList[Series[(1 - x) (4 + 9 x + 4 x^2)/(1 - 4 x^2 + x^4), {x, 0, 40}], x] (* _Vincenzo Librandi_, Feb 07 2014 *)

%t LinearRecurrence[{0,4,0,-1},{4,5,11,16},40] (* _Harvey P. Dale_, Oct 23 2015 *)

%K nonn,easy

%O 0,1

%A _Wolfdieter Lang_, Nov 08 2002

%E More terms from _Colin Barker_, Feb 06 2014

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Last modified December 6 19:22 EST 2019. Contains 329809 sequences. (Running on oeis4.)