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A077412
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Chebyshev U(n,x) polynomial evaluated at x=8.
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9
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1, 16, 255, 4064, 64769, 1032240, 16451071, 262184896, 4178507265, 66593931344, 1061324394239, 16914596376480, 269572217629441, 4296240885694576, 68470281953483775, 1091228270370045824, 17391182043967249409
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| For positive n, a(n) equals the permanent of the nXn tridiagonal matrix with 16's along the main diagonal, and i's along the superdiagonal and the subdiagonal (i is the imaginary unit). [From John M. Campbell, Jul 08 2011]
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LINKS
| Index entries for sequences related to linear recurrences with constant coefficients, signature (16,-1).
Tanya Khovanova, Recursive Sequences
Index entries for sequences related to Chebyshev polynomials.
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FORMULA
| a(n) = 16*a(n-1) - a(n-2), n>=1, a(-1)=0, a(0)=1.
a(n) = S(n, 16) with S(n, x) := U(n, x/2), Chebyshev's polynomials of the second kind. See A049310.
G.f.: 1/(1-16*x+x^2).
a(n) = (((8+3*sqrt(7))^(n+1) - (8-3*sqrt(7))^(n+1)))/(6*sqrt(7)).
a(n) = sqrt(A001081(n+1)^2-1)/63).
a(n) = Sum_{k, 0<=k<=n} A101950(n,k)*15^k. - DELEHAM Philippe, Feb 10 2012
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MATHEMATICA
| lst={}; Do[AppendTo[lst, GegenbauerC[n, 1, 8]], {n, 0, 8^2}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Sep 11 2008]
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PROG
| sage: [lucas_number1(n, 16, 1) for n in xrange(1, 20)] - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 25 2008
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CROSSREFS
| Sequence in context: A160446 A158531 A171321 * A206984 A135554 A017570
Adjacent sequences: A077409 A077410 A077411 * A077413 A077414 A077415
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KEYWORD
| nonn,easy,changed
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AUTHOR
| Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), Nov 08 2002
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