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Search: id:A030221
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| A030221 |
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Chebyshev even indexed U-polynomials evaluated at sqrt(7)/2. |
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+0
12
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| 1, 6, 29, 139, 666, 3191, 15289, 73254, 350981, 1681651, 8057274, 38604719, 184966321, 886226886, 4246168109, 20344613659, 97476900186, 467039887271, 2237722536169, 10721572793574, 51370141431701
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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a(n) = L(n,-5)*(-1)^n, where L is defined as in A108299; see also A004253 for L(n,+5). - Reinhard Zumkeller (reinhard.zumkeller(AT)lhsystems.com), Jun 01 2005
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REFERENCES
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W. Lang, On polynomials related to powers of the generating function of Catalan's numbers, Fib. Quart. 38,5 (2000) 408-419; Eq.(44), rhs, m=6.
K. Dilcher and K. B. Stolarsky, A Pascal-type triangle characterizing twin primes, Amer. Math. Monthly, 112 (2005), 673-681. (see page 678)
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LINKS
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Tanya Khovanova, Recursive Sequences
Index entries for sequences related to Chebyshev polynomials.
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FORMULA
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a(n) = 5*a(n-1)-a(n-2), a(-1)=-1, a(0)=1; a(n)=U(2*n, sqrt(7)/2); g.f.: (1+x)/(x^2-5*x+1); a(n)=A004254(n)+A004254(n+1)
a(n) ~ (1/2 + 1/6*sqrt(21))*(1/2*(5 + sqrt(21)))^n - Joe Keane (jgk(AT)jgk.org), May 16 2002
Let q(n, x)=sum(i=0, n, x^(n-i)*binomial(2*n-i, i)); then (-1)^n*q(n, -7)=a(n) - Benoit Cloitre (benoit7848c(AT)orange.fr), Nov 10 2002
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CROSSREFS
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Cf. A004253, A004254.
Adjacent sequences: A030218 A030219 A030220 this_sequence A030222 A030223 A030224
Sequence in context: A045445 A026884 A110311 this_sequence A009153 A012325 A125785
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KEYWORD
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nonn
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AUTHOR
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Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de)
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