0,2

Bisection (even part) of Chebyshev sequence with diophantine property.

b(n)^2 - 8*a(n)^2 = 17, with the companion sequence b(n)= A077240(n).

The odd part is A077413(n) with diophantine companion A077239(n).

I. Adler, Three diophantine equations - Part II, Fib. Quart., 7(1969), pps. 181-193.

A. H. Beiler, Recreations in the Theory of Numbers, Dover, N. Y., 1964, pps. 122-125, 194-196.

E. I. Emerson, Recurrent Sequences in the Equation DQ^2=R^2+N, Fib. Quart., 7(1969), pps. 231-242.

Tanya Khovanova, Recursive Sequences

Index entries for sequences related to Chebyshev polynomials.

a(n)=6*a(n-1)-a(n-2), a(0)=1, a(1)=8.

a(n)=((3 + 2*sqrt(2))^(n+1) - (3 - 2*sqrt(2))^(n+1) + 2*((3 + 2*sqrt(2))^n - (3 - 2*sqrt(2))^n))/(4*sqrt(2)).

a(n)= S(n, 6)+2*S(n-1, 6), with S(n, x) Chebyshev's polynomials of the second kind, A049310. S(n, 6)= A001109(n+1).

G.f.: (1+2*x)/(1-6*x+x^2).

8 = a(1) = sqrt((A077240(1)^2 - 17)/8) = sqrt((23^2 - 17)/8)= sqrt(64) = 8.

a[0]:=1: a[1]:=8: for n from 2 to 26 do a[n]:=6*a[n-1]-a[n-2] od: seq(a[n], n=0..20); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jul 26 2006

Cf. A002315 and A038761.

A077241 (even and odd parts).

Adjacent sequences: A054485 A054486 A054487 this_sequence A054489 A054490 A054491

Sequence in context: A016198 A051140 A014524 this_sequence A034349 A024108 A121028

easy,nonn

Barry E. Williams, May 04 2000

More terms from James A. Sellers (sellersj(AT)math.psu.edu), May 05 2000

Chebyshev comments from W. Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), Nov 08 2002