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Search: id:A099276
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| A099276 |
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Unsigned member r=-18 of the family of Chebyshev sequences S_r(n) defined in A092184. |
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+0
1
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| 0, 1, 18, 361, 7200, 143641, 2865618, 57168721, 1140508800, 22753007281, 453919636818, 9055639729081, 180658874944800, 3604121859166921, 71901778308393618, 1434431444308705441, 28616727107865715200
(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_{-18}(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)= 20*a(n-1)-a(n-2)+2*(-1)^(n+1), n>=2, a(0)=0, a(1)=1.
a(n)= 19*a(n-1) + 19*a(n-2) - a(n-3), n>=3, a(0)=0, a(1)=1, a(2)=18.
G.f.: x*(1-x)/((1+x)*(1-20*x+x^2)) = x*(1-x)/(1-19*x-19*x^2+x^3) (from the Stephan link, see A092184).
a(n)= (T(n, 10)-(-1)^n)/11, with Chebyshev's polynomials of the first kind evaluated at x=10: T(n, 10)=A001085(n)=((10+3*sqrt(11))^n + (10-3*sqrt(11))^n)/2.
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CROSSREFS
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Sequence in context: A143168 A127585 A086502 this_sequence A070943 A159647 A111454
Adjacent sequences: A099273 A099274 A099275 this_sequence A099277 A099278 A099279
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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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