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Search: id:A098305
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| A098305 |
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Unsigned member r=-5 of the family of Chebyshev sequences S_r(n) defined in A092184. |
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+0
1
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| 0, 1, 5, 36, 245, 1681, 11520, 78961, 541205, 3709476, 25425125, 174266401, 1194439680, 8186811361, 56113239845, 384605867556, 2636127833045, 18068288963761, 123841894913280, 848824975429201, 5817932933091125
(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_{-5}(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, 7/2)-(-1)^n)/9, with twice the Chebyshev's polynomials of the first kind evaluated at x=7/2: 2*T(n, 7/2)=A056854(n)= ((7+sqrt(45))^n + (7-sqrt(45))^n)/2^n.
a(n)= 7*a(n-1)-a(n-2)+2*(-1)^(n+1), n>=2, a(0)=0, a(1)=1.
a(n)= 6*a(n-1) + 6*a(n-2) - a(n-3), n>=3, a(0)=0, a(1)=1, a(2)=5.
G.f.: x*(1-x)/((1+x)*(1-7*x+x^2)) = x*(1-x)/(1-6*x-6*x^2+x^3) (from the Stephan link, see A092184).
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CROSSREFS
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Sequence in context: A048535 A015547 A067376 this_sequence A055270 A164110 A052203
Adjacent sequences: A098302 A098303 A098304 this_sequence A098306 A098307 A098308
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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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