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Search: id:A099272
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| A099272 |
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Unsigned member r=-14 of the family of Chebyshev sequences S_r(n) defined in A092184. |
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1
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| 0, 1, 14, 225, 3584, 57121, 910350, 14508481, 231225344, 3685097025, 58730327054, 936000135841, 14917271846400, 237740349406561, 3788928318658574, 60385112749130625, 962372875667431424, 15337580897929772161
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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((-1)^(n+1))*a(n) = S_{-14}(n), n>=0, defined in A092184.
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LINKS
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Index entries for sequences related to Chebyshev polynomials.
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FORMULA
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a(n)= (T(n, 8)-(-1)^n)/9, with Chebyshev's polynomials of the first kind evaluated at x=8: T(n, 8)=A001081(n)=((8+3*sqrt(7))^n + (8-3*sqrt(7))^n)/2.
a(n)= 16*a(n-1)-a(n-2)+2*(-1)^(n+1), n>=2, a(0)=0, a(1)=1.
a(n)= 15*a(n-1) + 15*a(n-2) - a(n-3), n>=3, a(0)=0, a(1)=1, a(2)=14.
G.f.: x*(1-x)/((1+x)*(1-16*x+x^2)) = x*(1-x)/(1-15*x-15*x^2+x^3) (from the Stephan link, see A092184).
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CROSSREFS
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Sequence in context: A113894 A145269 A027774 this_sequence A120048 A079563 A166774
Adjacent sequences: A099269 A099270 A099271 this_sequence A099273 A099274 A099275
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KEYWORD
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nonn,easy
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AUTHOR
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Wolfdieter Lang (wolfdieter.lang_AT_physik_DOT_uni-karlsruhe_DOT_de), Oct 18 2004
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