0,2

a(15+30k)-1 and a(15+30k)+1 are consecutive odd powerful numbers. The first pair is 13837575261124+-1. See A076445. - T. D. Noe (noe(AT)sspectra.com), May 04 2006

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

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.

H. Brocard, Notes e'le'mentaires sur le proble`me de Peel, Nouvelles Correspondance Math\'{e}matique, 4 (1878), 161-169.

T. D. Noe, Table of n, a(n) for n=0..200

Index entries for sequences related to linear recurrences with constant coefficients

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 sequences related to Chebyshev polynomials.

For all elements x of the sequence, 15*x^2 -15 is a square. Lim. n -> Inf. a(n)/a(n-1) = 4 + sqrt(15). - Gregory V. Richardson (omomom(AT)hotmail.com), Oct 11 2002

a(n) = ((4+sqrt(15))^n + (4-sqrt(15))^n)/2.

a(n) = 4*S(n-1, 8)-S(n-2, 8) = (S(n, 8)-S(n-2, 8))/2, n>=1; S(n, x) := U(n, x/2) with Chebyshev's polynomials of the 2nd kind, A049310, with S(-1, x) := 0 and S(-2, x) := -1.

a(n) = T(n, 4) with Chebyshev's polynomials of the first kind; see A053120.

G.f.: (1-4*x)/(1-8*x+x^2). a(n)=a(-n). - R. Stephan, Jun 06 2005

a(n)a(n+3) - a(n+1)a(n+2) = 120. - R. Stephan, Jun 06 2005

A001091:=-(-1+4*z)/(1-8*z+z**2); [Conjectured by S. Plouffe in his 1992 dissertation.]

(PARI) a(n)=subst(poltchebi(n), x, 4)

(PARI) a(n)=n=abs(n); polcoeff((1-4*x)/(1-8*x+x^2)+x*O(x^n), n) /* Michael Somos Jun 07 2005 */

a(n) = sqrt{15*[(A001090(n))^2]+1}.

Sequence in context: A014537 A136284 A039765 this_sequence A077615 A025506 A039306

Adjacent sequences: A001088 A001089 A001090 this_sequence A001092 A001093 A001094

nonn,easy

N. J. A. Sloane (njas(AT)research.att.com).

More terms from Larry Reeves (larryr(AT)acm.org), Aug 25 2000

Chebyshev comments from W. Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), Oct 31 2002