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

0,1

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

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).

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

Example

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

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 *)

Crossrefs

Sequence in context: A066898 A118143 A001350 * A185507 A000286 A227620

Adjacent sequences: A077235 A077236 A077237 * A077239 A077240 A077241

Keyword

nonn,easy

Author

Wolfdieter Lang, Nov 08 2002

Extensions

More terms from Colin Barker, Feb 06 2014

Status

approved