0,1

S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures}, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.

A. F. Horadam, Generating identities for generalized Fibonacci and Lucas triples, Fib. Quart., 15 (1977), 289-292.

S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures}, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.

S. Plouffe, 1031 Generating Functions and Conjectures, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.

Tanya Khovanova, Recursive Sequences

Index entries for recurrences a(n) = k*a(n - 1) +/- a(n - 2)

Index entries for sequences related to Chebyshev polynomials.

a(n) = [(3 + sqrt13)/2]^n + [(3 - sqrt13)/2]^n; A006190(n-2) + A006190(n) = a(n-1); [a(n)]^2 - 13[A006190(n)]^2 = 4(-1)^n. - Gary W. Adamson (qntmpkt(AT)yahoo.com), Jun 15 2003

E.g.f. : 2exp(3x/2)cosh(sqrt(13)x/2); a(n)=2^(1-n)sum{k=0..floor(n/2), C(n, 2k)13^k3^(n-2k)}. a(n)=2T(n, 3i/2)(-i)^n with T(n, x) Chebyshev's polynomials of the first kind (see A053120) and i^2=-1. - Paul Barry (pbarry(AT)wit.ie), Nov 15 2003

A006497:=(-2+3*z)/(-1+3*z+z**2); [Conjectured by S. Plouffe in his 1992 dissertation.]

Cf. A006190.

Cf. A100230.

Sequence in context: A080155 A032357 A062630 this_sequence A038912 A019361 A093804

Adjacent sequences: A006494 A006495 A006496 this_sequence A006498 A006499 A006500

nonn,easy

njas

More terms from Ray Chandler (rayjchandler(AT)sbcglobal.net), Feb 14 2004