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Search: id:A098308
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| A098308 |
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Unsigned member r=-8 of the family of Chebyshev sequences S_r(n) defined in A092184. |
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+0
1
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| 0, 1, 8, 81, 800, 7921, 78408, 776161, 7683200, 76055841, 752875208, 7452696241, 73774087200, 730288175761, 7229107670408, 71560788528321, 708378777612800, 7012226987599681, 69413891098384008, 687126683996240401
(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_{-8}(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)= (T(n, 5)-(-1)^n)/6, with Chebyshev's polynomials of the first kind evaluated at x=5: T(n, 5)=A001079(n)=((5+2*sqrt(6))^n + (5-2*sqrt(6))^n)/2.
a(n)= 10*a(n-1)-a(n-2)+2*(-1)^(n+1), n>=2, a(0)=0, a(1)=1.
a(n)= 9*a(n-1) + 9*a(n-2) - a(n-3), n>=3, a(0)=0, a(1)=1, a(2)=8.
G.f.: x*(1-x)/((1+x)*(1-10*x+x^2)) = x*(1-x)/(1-9*x-9*x^2+x^3) (from the Stephan link, see A092184).
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CROSSREFS
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Sequence in context: A078292 A027768 A007792 this_sequence A055996 A068617 A007778
Adjacent sequences: A098305 A098306 A098307 this_sequence A098309 A098310 A098311
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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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