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A098310
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Unsigned member r=-11 of the family of Chebyshev sequences S_r(n) defined in A092184.
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0
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0, 1, 11, 144, 1859, 24025, 310464, 4012009, 51845651, 669981456, 8657913275, 111882891121, 1445819671296, 18683772835729, 241443227193179, 3120078180675600, 40319573121589619, 521034372399989449
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OFFSET
| 0,3
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COMMENTS
| ((-1)^(n+1))*a(n) = S_{-11}(n), n>=0, defined in A092184.
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LINKS
| Index entries for sequences related to Chebyshev polynomials.
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FORMULA
| a(n)= 2*(T(n, 13/2)-(-1)^n)/15, with twice Chebyshev's polynomials of the first kind evaluated at x=13/2: 2*T(n, 13/2)=A078363(n)=((13+sqrt(165))^n + (13-sqrt(165))^n)/2^n.
a(n)= 13*a(n-1)-a(n-2)+2*(-1)^(n+1), n>=2, a(0)=0, a(1)=1.
a(n)= 12*a(n-1) + 12*a(n-2) - a(n-3), n>=3, a(0)=0, a(1)=1, a(2)=11.
G.f.: x*(1-x)/((1+x)*(1-13*x+x^2)) = x*(1-x)/(1-12*x-12*x^2+x^3) (from the Stephan link, see A092184).
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CROSSREFS
| Sequence in context: A015687 A051583 A027771 * A061613 A093750 A194726
Adjacent sequences: A098307 A098308 A098309 * A098311 A098312 A098313
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KEYWORD
| nonn,easy
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AUTHOR
| Wolfdieter Lang (wolfdieter.lang_AT_physik_DOT_uni-karlsruhe_DOT_de), Oct 18 2004
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