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Search: id:A097732
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| A097732 |
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Pell equation solutions (7*a(n))^2 - 2*(5*b(n))^2 = -1 with b(n):=A097733(n), n>=0. Note that D=50=2*5^2 is not square-free. |
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3
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| 1, 199, 39401, 7801199, 1544598001, 305822602999, 60551330795801, 11988857674965599, 2373733268312392801, 469987198268178808999, 93055091523831091789001, 18424438134520287995413199
(list; graph; listen)
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OFFSET
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0,2
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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)= S(n, 2*99) + S(n-1, 2*99) = S(2*n, 10*sqrt(2)), with Chebyshev polynomials of the 2nd kind. See A049310 for the triangle of S(n, x)= U(n, x/2) coefficients. S(-1, x) := 0 =: U(-1, x).
G.f.: (1+x)/(1-2*99*x+x^2).
a(n)= ((-1)^n)*T(2*n+1, 7*I)/(7*I) with the imaginary unit I and Chebyshev polynomials of the first kind. See the T-triangle A053120.
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EXAMPLE
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(x,y) = (7,1), (1393,197), (275807,39005), ... give the positive integer solutions to x^2 - 50*y^2 =-1.
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CROSSREFS
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Cf. A097731 for S(n, 2*99).
Adjacent sequences: A097729 A097730 A097731 this_sequence A097733 A097734 A097735
Sequence in context: A086977 A069244 A052355 this_sequence A028482 A111472 A033523
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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), Aug 31 2004
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