A077237 - OEIS

%I #12 Feb 12 2017 02:12:20

%S 1,2,6,9,23,34,86,127,321,474,1198,1769,4471,6602,16686,24639,62273,

%T 91954,232406,343177,867351,1280754,3236998,4779839,12080641,17838602,

%U 45085566,66574569,168261623

%N Combined Diophantine Chebyshev sequences A054491 and A077234.

%C -3*a(n)^2 + b(n)^2 = 13, with the companion sequence b(n)= A077238(n).

%H Matthew House, <a href="/A077237/b077237.txt">Table of n, a(n) for n = 0..3478</a>

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

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,4,0,-1).

%F a(2*k)= A054491(k) and a(2*k+1)= A077234(k), k>=0.

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

%F a(n) = 4*a(n-2) - a(n-4). - _Matthew House_, Feb 11 2017

%e 3*a(2)^2 + 13 = 3*36+13 = 121 = 11^2 = A077238(2)^2.

%t CoefficientList[Series[(1 + x) (1 + x + x^2)/(1 - 4 x^2 + x^4), {x, 0, 28}], x] (* _Michael De Vlieger_, Feb 11 2017 *)

%K nonn,easy

%O 0,2

%A _Wolfdieter Lang_, Nov 08 2002