A077248 Combined Diophantine Chebyshev sequences A077246 and A077244.

2, 3, 13, 22, 102, 173, 803, 1362, 6322, 10723, 49773, 84422, 391862, 664653, 3085123, 5232802, 24289122, 41197763, 191227853, 324349302, 1505533702, 2553596653, 11853041763, 20104423922, 93318800402

Offset

0,1

Comments

3*a(n)^2 - 5*b(n)^2 = 7, with the companion sequence b(n)= A077247(n).

Positive values of x (or y) satisfying x^2 - 8xy + y^2 + 35 = 0. - Colin Barker, Feb 08 2014

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index entries for sequences related to Chebyshev polynomials.

Formula

a(2*k)= A077246(k) and a(2*k+1)= A077244(k), k>=0.

G.f.: (1-x)*(2+x)*(1+2*x)/(1-8*x^2+x^4).

Example

13 = a(2) = sqrt((5*A077247(2)^2 + 7)/3) = sqrt((5*10^2 + 7)/3)= sqrt(169) = 13.

Mathematica

CoefficientList[Series[(1 - x) (2 + x) (1 + 2 x)/(1 - 8 x^2 + x^4), {x, 0, 30}], x] (* Vincenzo Librandi, Feb 11 2014 *)

Crossrefs

Sequence in context: A019226 A138699 A341713 * A282342 A137248 A355438

Adjacent sequences: A077245 A077246 A077247 * A077249 A077250 A077251

Keyword

nonn,easy

Author

Wolfdieter Lang, Nov 08 2002

Status

approved