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Search: id:A099273
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| A099273 |
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Unsigned member r=-15 of the family of Chebyshev sequences S_r(n) defined in A092184. |
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+0
1
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| 0, 1, 15, 256, 4335, 73441, 1244160, 21077281, 357069615, 6049106176, 102477735375, 1736072395201, 29410752983040, 498246728316481, 8440783628397135, 142995074954434816, 2422475490596994735
(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_{-15}(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, 17/2)-(-1)^n)/19, with twice Chebyshev's polynomials of the first kind evaluated at x=17/2: 2*T(n, 17/2)=A078367(n)= ((17+sqrt(285))^n +(17-sqrt(285))^n)/2^n.
a(n)= 17*a(n-1)-a(n-2)+2*(-1)^(n+1), n>=2, a(0)=0, a(1)=1.
a(n)= 16*a(n-1) + 16*a(n-2) - a(n-3), n>=3, a(0)=0, a(1)=1, a(2)=15.
G.f.: x*(1-x)/((1+x)*(1-17*x+x^2)) = x*(1-x)/(1-16*x-16*x^2+x^3) (from the Stephan link, see A092184).
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CROSSREFS
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Sequence in context: A015691 A145562 A027775 this_sequence A013381 A013384 A013380
Adjacent sequences: A099270 A099271 A099272 this_sequence A099274 A099275 A099276
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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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