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Search: id:A099270
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| A099270 |
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Unsigned member r=-12 of the family of Chebyshev sequences S_r(n) defined in A092184. |
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+0
1
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| 0, 1, 12, 169, 2352, 32761, 456300, 6355441, 88519872, 1232922769, 17172398892, 239180661721, 3331356865200, 46399815451081, 646266059449932, 9001325016847969, 125372284176421632, 1746210653453054881
(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_{-12}(n), n>=0, defined in A092184.
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LINKS
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Index entries for two-way infinite sequences
Index entries for sequences related to Chebyshev polynomials.
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FORMULA
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a(n)= (T(n, 7)-(-1)^n)/8, with Chebyshev's polynomials of the first kind evaluated at x=7: T(n, 7)=A011943(n)=((7+4*sqrt(3))^n + (7-4*sqrt(3))^n)/2.
a(n)= 13*a(n-1) + 13*a(n-2) - a(n-3), n>=3, a(0)=0, a(1)=1, a(2)=12.
G.f.: x*(1-x)/((1+x)*(1-14*x+x^2)) = x*(1-x)/(1-13*x-13*x^2+x^3) (from the Stephan link, see A092184).
a(n)=14*a(n-1)-a(n-2)-2*(-1)^n, a(0)=0, a(1)=1. a(-n)=a(n).
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PROGRAM
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(PARI) a(n)=real(((7+4*quadgen(12))^n-(-1)^n)/8) /* Michael Somos Apr 30 2005 */
(PARI) a(n)=n=abs(2*n); round(2^(n-4)*prod(k=1, n, 2-sin(2*Pi*k/n)))
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CROSSREFS
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Sequence in context: A071103 A012489 A027772 this_sequence A120662 A099930 A052208
Adjacent sequences: A099267 A099268 A099269 this_sequence A099271 A099272 A099273
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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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