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Search: id:A078987
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| A078987 |
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Chebyshev U(n,x) polynomial evaluated at x=19. |
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+0
5
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| 1, 38, 1443, 54796, 2080805, 79015794, 3000519367, 113940720152, 4326746846409, 164302439443390, 6239165952002411, 236924003736648228, 8996872976040630253, 341644249085807301386, 12973484592284636822415
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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A078986(n+1)^2 - 10*(6*a(n))^2 = +1, n>=0, (Pell equation +1, see A033313 and A033317).
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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) = 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)).
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MATHEMATICA
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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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PROGRAM
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(Other) sage: [lucas_number1(n, 38, 1) for n in xrange(1, 16)]# [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Nov 07 2009]
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CROSSREFS
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Sequence in context: A137030 A027657 A158702 this_sequence A009982 A041685 A158766
Adjacent sequences: A078984 A078985 A078986 this_sequence A078988 A078989 A078990
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KEYWORD
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nonn,easy,new
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AUTHOR
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Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), Jan 10 2003
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