Search: id:A025170
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%I A025170
%S A025170 1,2,5,28,11,230,559,952,6935,5302,51811,151340,163619,
%T A025170 1689298,1906025,11391632,39937489,22649710,404736821,605626252,
%U A025170 2431378885,10313394038,1255621889,95331790120,179362983239
%V A025170 1,-2,-5,28,-11,-230,559,952,-6935,5302,51811,-151340,-163619,
%W A025170 1689298,-1906025,-11391632,39937489,22649710,-404736821,605626252,
%X A025170 2431378885,-10313394038,-1255621889,95331790120,-179362983239
%N A025170 G.f.: 1/(1+2x+9x^2).
%C A025170 Reciprocal Chebyshev polynomial of second kind evaluated at 3 multiplied 
               by (-1)^n.
%C A025170 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
%H A025170 <a href="Sindx_Rea.html#recLCC">Index entries for sequences related to 
               linear recurrences with constant coefficients</a>
%H A025170 <a href="Sindx_Ch.html#Cheby">Index entries for sequences related to 
               Chebyshev polynomials.</a>
%F A025170 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
%F A025170 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
%F A025170 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]
%t A025170 Table[ 3^n ChebyshevU[ n, -1/3 ], {n, 0, 24} ]
%o A025170 (PARI) a(n)=if(n<0,0,polcoeff(1/(1+2*x+9*x^2)+x*O(x^n),n))
%o A025170 (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 */
%o A025170 (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 */
%Y A025170 Cf. A087455, A088137.
%Y A025170 Sequence in context: A057438 A002795 A127357 this_sequence A151775 A095159 
               A047132
%Y A025170 Adjacent sequences: A025167 A025168 A025169 this_sequence A025171 A025172 
               A025173
%K A025170 sign
%O A025170 0,2
%A A025170 w.meeussen (wouter.meeussen(AT)pandora.be)
%E A025170 More terms from Creighton Dement (creighton.k.dement(AT)uni-oldenburg.de), 
               Aug 22 2004

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