0,2

This is the r=7 member in the r-family of sequences S_r(n+1) defined in A092184 where more information can be found.

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.

R. Stephan, Boring proof of a nonlinearity

Index entries for sequences related to Chebyshev polynomials.

a(n)=5a(n-1)-a(n-2)+2, a(0)=1, a(1)=7.

a(n) = 1/3*{-2+[(5+sqrt(21))/2]^n+[(5-sqrt(21))/2]^n}. - R. Stephan, Apr 14 2004

G.f.: (1+x)/((1-x)*(1-5*x+x^2))=(1+x)/(1-6*x+6*x^2-x^3). From the R. Stephan link.

a(n)= 6*a(n-1)-6*a(n-2)+a(n-3), n>=2, a(-1):=0, a(0)=1, a(1)=7.

a(n)=2*T(n, 5/2)-2, with twice the Chebyshev's polynomials of the first kind, 2*T(n, x=5/2)=A003501(n).

a(n)= b(n) + b(n-1), n>=1, with b(n):=A089817(n) the partial sums of S(n, 5)= U(n, 5/2)=A004254(n+1), with S(n, x)=U(n, x/2) Chebyshev's polynomials of the second kind.

A004254 = sqrt{21*(A054493)^2+28*(A054493)}/7.

Cf. A004254.

Sequence in context: A102053 A058681 A110310 this_sequence A037538 A037482 A147546

Adjacent sequences: A054490 A054491 A054492 this_sequence A054494 A054495 A054496

easy,nonn

Barry E. Williams, May 06 2000

More terms from James A. Sellers (sellersj(AT)math.psu.edu), May 10 2000

Chebyshev comments from W. Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), Sep 10 2004