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A078987
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Chebyshev U(n,x) polynomial evaluated at x=19.
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5
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1, 38, 1443, 54796, 2080805, 79015794, 3000519367, 113940720152, 4326746846409, 164302439443390, 6239165952002411, 236924003736648228, 8996872976040630253, 341644249085807301386, 12973484592284636822415
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| A078986(n+1)^2 - 10*(6*a(n))^2 = +1, n>=0, (Pell equation +1, see A033313 and A033317).
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LINKS
| Tanya Khovanova, Recursive Sequences
Index entries for sequences related to Chebyshev polynomials.
Index to sequences with linear recurrences with constant coefficients, signature (38,-1).
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FORMULA
| a(n) = 38*a(n-1) - a(n-2), n>=1, a(-1)=0, a(0)=1.
a(n) = S(n, 38) with S(n, x) := U(n, x/2), Chebyshev's polynomials of the second kind. See A049310.
G.f.: 1/(1-38*x+x^2).
a(n)= sum((-1)^k*binomial(n-k, k)*38^(n-2*k), k=0..floor(n/2)).
a(n) = ((19+6*sqrt(10))^(n+1) - (19-6*sqrt(10))^(n+1))/(12*sqrt(10)).
a(n) = Sum_{k, 0<=k<=n} A101950(n,k)*37^k. - DELEHAM Philippe, Feb 10 2012
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MATHEMATICA
| lst={}; Do[AppendTo[lst, GegenbauerC[n, 1, 19]], {n, 0, 8^2}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Sep 11 2008]
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PROG
| (Other) sage: [lucas_number1(n, 38, 1) for n in xrange(1, 16)]# [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Nov 07 2009]
(PARI) a(n)=subst(polchebyshev(n, 2), x, 19) \\ Charles R Greathouse IV, Feb 10 2012
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CROSSREFS
| Sequence in context: A170719 A170757 A158702 * A009982 A041685 A158766
Adjacent sequences: A078984 A078985 A078986 * A078988 A078989 A078990
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KEYWORD
| nonn,easy,changed
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AUTHOR
| Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), Jan 10 2003
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