0,2

Reciprocal Chebyshev polynomial of second kind evaluated at 3 multiplied by (-1)^n.

a(n) is (-1)^n times the determinant of the following tri-diagonal n X n matrix : [2 3 0 0 ... ] [3 2 3 0 ... ] [0 3 2 3 0 ... ] [. 0 3 2 3 ... ] [. . . . . ] [. . . 3 2 3 0] [. . . 0 3 2 3] [. . . 0 0 3 2] - Sharon Sela (sharonsela(AT)hotmail.com), Jan 19 2002

Index entries for sequences related to linear recurrences with constant coefficients

Index entries for sequences related to Chebyshev polynomials.

a(n) = ( A088137(n+1) )^2 + ( A087455(n+1)/2 )^2 - ( A087455(n+2)/2 )^2. - Creighton Dement (creighton.k.dement(AT)uni-oldenburg.de), Aug 20 2004

A025170(n) = ( A088137(n+1) )^2 + ( A087455(n+1)/2 )^2 - ( A087455(n+2)/2 )^2. Using the known formula ( see A088137 ) |3*A087455(n) - A087455(n+1)| = 2*A088137(n+1) or 3*A087455(n) + A087455(n+1) = 2*A088137(n+1) A025170 can be expressed entirely using A087455 - Creighton Dement (creighton.k.dement(AT)uni-oldenburg.de), Aug 22 2004

a(0)=1, a(1)=-2, a(n) = -(2*a(n-1)+9*a(n-2)) for n>1. [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Sep 19 2009]

Table[ 3^n ChebyshevU[ n, -1/3 ], {n, 0, 24} ]

(PARI) a(n)=if(n<0, 0, polcoeff(1/(1+2*x+9*x^2)+x*O(x^n), n))

(PARI) a(n)=if(n<0, 0, 3^n*subst(poltchebi(n+1)+3*poltchebi(n), 'x, -1/3)*3/8) /* Michael Somos Sep 15 2005 */

(PARI) a(n)=if(n<0, 0, (-1)^n*matdet(matrix(n, n, i, j, if(abs(i-j)<2, 2+abs(i-j))))) /* Michael Somos Sep 15 2005 */

Cf. A087455, A088137.

Sequence in context: A057438 A002795 A127357 this_sequence A151775 A095159 A047132

Adjacent sequences: A025167 A025168 A025169 this_sequence A025171 A025172 A025173

sign

w.meeussen (wouter.meeussen(AT)pandora.be)

More terms from Creighton Dement (creighton.k.dement(AT)uni-oldenburg.de), Aug 22 2004