0,3

This is the r=9 member of the r-family of sequences S_r(n) defined in A092184 where more information can be found.

A. T. Benjamin and J. J. Quinn, Proofs that really count: the art of combinatorial proof, M.A.A. 2003, id. 27.

R. Stephan, Boring proof of a nonlinearity

Index entries for sequences related to Chebyshev polynomials.

G.f.: (x+x^2)/((1-x)*(1-7*x+x^2)).

a(n) = 8*a(n-1)-8*a(n-2)+a(n-3), n>2. a(0) = 0, a(1) = 1, a(2) = 9.

a(n) = 7a(n-1)-a(n-2)+2 = A001906(n)^2.

a(n) = 1/5*{-2+[(7+sqrt(45))/2]^n+[(7-sqrt(45))/2]^n}. - R. Stephan, Apr 14 2004

a(n)= 2*(T(n, 7/2)-1)/5 with twice the Chebyshev's polynomials of the first kind evaluated at x=7/2: 2*T(n, 7/2)= A056854(n). W. Lang (wolfdieter.lang_AT_physik_DOT_uni-karlsruhe_DOT_de), Oct 18 2004

F(2) + F(6) + F(10) +...+ F(4n+2) = F(2n+1)*F(2n+3) - 1.

(PARI) a(n)=fibonacci(2*n)^2

(Mupad) numlib::fibonacci(2*n)^2 $ n = 0..35; - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 13 2008

(Other) sage: [(fibonacci(2*n))^2 for n in xrange(0, 21)]# [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 15 2009]

A049684(n)=(A000032(4*n)-2)/5. First differences give A033890.

a(n) = A064170(n+2) - 1 = (1/5) A081070. Bisection of A007598 and A064841.

First differences of A103434.

Sequence in context: A143631 A083328 A000846 this_sequence A037540 A037484 A013566

Adjacent sequences: A049681 A049682 A049683 this_sequence A049685 A049686 A049687

nonn,easy,nice

Clark Kimberling (ck6(AT)evansville.edu)

Better description and more terms from Michael Somos