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Search: id:A099277
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| A099277 |
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Unsigned member r=-19 of the family of Chebyshev sequences S_r(n) defined in A092184. |
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+0
1
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| 0, 1, 19, 400, 8379, 175561, 3678400, 77070841, 1614809259, 33833923600, 708897586339, 14853015389521, 311204425593600, 6520439922076081, 136618033938004099, 2862458272776010000, 59975005694358205899
(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_{-19}(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)= 2*(T(n, 21/2)-(-1)^n)/23, with twice Chebyshev's polynomials of the first kind evaluated at x=21/2: 2*T(n, 21/2)=A090729(n)= ((21+sqrt(437))^n + (21-sqrt(437))^n)/2^n.
a(n)= 21*a(n-1)-a(n-2)+2*(-1)^(n+1), n>=2, a(0)=0, a(1)=1.
a(n)= 20*a(n-1) + 20*a(n-2) - a(n-3), n>=3, a(0)=0, a(1)=1, a(2)=19.
G.f.: x*(1-x)/((1+x)*(1-21*x+x^2)) = x*(1-x)/(1-20*x-20*x^2+x^3) (from the Stephan link, see A092184).
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CROSSREFS
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Sequence in context: A094737 A009075 A015694 this_sequence A069612 A077716 A089573
Adjacent sequences: A099274 A099275 A099276 this_sequence A099278 A099279 A099280
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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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