A077238 Combined Diophantine Chebyshev sequences A077236 and A077235.

4, 5, 11, 16, 40, 59, 149, 220, 556, 821, 2075, 3064, 7744, 11435, 28901, 42676, 107860, 159269, 402539, 594400, 1502296, 2218331, 5606645, 8278924, 20924284, 30897365, 78090491, 115310536, 291437680, 430344779, 1087660229, 1606068580, 4059203236, 5993929541

Offset: 0

Author

Wolfdieter Lang, Nov 08 2002

Keywords

• nonn
• easy

Comments

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

Positive values of x (or y) satisfying x^2 - 4xy + y^2 + 39 = 0. - Colin Barker, Feb 06 2014

Positive values of x (or y) satisfying x^2 - 14xy + y^2 + 624 = 0. - Colin Barker, Feb 16 2014

Examples

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

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• 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) (4 + 9 x + 4 x^2)/(1 - 4 x^2 + x^4), {x, 0, 40}], x] (* Vincenzo Librandi, Feb 07 2014 *)
LinearRecurrence[{0,4,0,-1},{4,5,11,16},40] (* Harvey P. Dale, Oct 23 2015 *)

Formula

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

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

a(n) = 4*a(n-2)-a(n-4). - Colin Barker, Feb 06 2014

Extensions

More terms from Colin Barker, Feb 06 2014