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A077248 Combined Diophantine Chebyshev sequences A077246 and A077244. 3
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 (list; graph; refs; listen; history; text; internal format)
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: A139563 A019226 A138699 * A282342 A137248 A136260

Adjacent sequences:  A077245 A077246 A077247 * A077249 A077250 A077251

KEYWORD

nonn,easy

AUTHOR

Wolfdieter Lang, Nov 08 2002

STATUS

approved

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Last modified December 6 04:14 EST 2019. Contains 329784 sequences. (Running on oeis4.)