A077237 Combined Diophantine Chebyshev sequences A054491 and A077234.

1, 2, 6, 9, 23, 34, 86, 127, 321, 474, 1198, 1769, 4471, 6602, 16686, 24639, 62273, 91954, 232406, 343177, 867351, 1280754, 3236998, 4779839, 12080641, 17838602, 45085566, 66574569, 168261623

Offset: 0

Author

Wolfdieter Lang, Nov 08 2002

Keywords

• nonn
• easy

Comments

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

Examples

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

Links

• Matthew House, Table of n, a(n) for n = 0..3478
• Index entries for sequences related to Chebyshev polynomials.
• Index entries for linear recurrences with constant coefficients, signature (0,4,0,-1).

Programs

Mathematica

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

Formula

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

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

a(n) = 4*a(n-2) - a(n-4). - Matthew House, Feb 11 2017