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Search: id:A098309
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| A098309 |
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Unsigned member r=-10 of the family of Chebyshev sequences S_r(n) defined in A092184. |
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+0
1
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| 0, 1, 10, 121, 1440, 17161, 204490, 2436721, 29036160, 345997201, 4122930250, 49129165801, 585427059360, 6975995546521, 83126519498890, 990542238440161, 11803380341783040, 140650021862956321, 1675996882013692810
(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_{-10}(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, 6)-(-1)^n)/7, with Chebyshev's polynomials of the first kind evaluated at x=6: T(n, 6)=A023038(n)=((6+sqrt(35))^n + (6-sqrt(35))^n)/2.
a(n)= 12*a(n-1)-a(n-2)+2*(-1)^(n+1), n>=2, a(0)=0, a(1)=1.
a(n)= 11*a(n-1) + 11*a(n-2) - a(n-3), n>=3, a(0)=0, a(1)=1, a(2)=10.
G.f.: x*(1-x)/((1+x)*(1-12*x+x^2)) = x*(1-x)/(1-11*x-11*x^2+x^3) (from the Stephan link, see A092184).
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CROSSREFS
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Sequence in context: A111695 A027770 A091692 this_sequence A056116 A081784 A005174
Adjacent sequences: A098306 A098307 A098308 this_sequence A098310 A098311 A098312
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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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