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A098307
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Unsigned member r=-7 of the family of Chebyshev sequences S_r(n) defined in A092184.
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0
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0, 1, 7, 64, 567, 5041, 44800, 398161, 3538647, 31449664, 279508327, 2484125281, 22077619200, 196214447521, 1743852408487, 15498457228864, 137742262651287, 1224181906632721, 10879894897043200, 96694872166756081
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OFFSET
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0,3
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COMMENTS
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((-1)^(n+1))*a(n) = S_{-7}(n), n>=0, defined in A092184.
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LINKS
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FORMULA
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a(n)= 2*(T(n, 9/2)-(-1)^n)/11, with twice Chebyshev's polynomials of the first kind evaluated at x=9/2: 2*T(n, 9/2)=A056918(n)=((9+sqrt(77))^n + (9-sqrt(77))^n)/2^n.
a(n)= 9*a(n-1)-a(n-2)+2*(-1)^(n+1), n>=2, a(0)=0, a(1)=1.
a(n)= 8*a(n-1) + 8*a(n-2) - a(n-3), n>=3, a(0)=0, a(1)=1, a(2)=7.
G.f.: x*(1-x)/((1+x)*(1-9*x+x^2)) = x*(1-x)/(1-8*x-8*x^2+x^3) (from the Stephan link, see A092184).
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MATHEMATICA
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LinearRecurrence[{8, 8, -1}, {0, 1, 7}, 20] (* Harvey P. Dale, Jan 01 2017 *)
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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