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Search: id:A098252
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| A098252 |
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Chebyshev polynomials S(n,363) + S(n-1,363) with Diophantine property. |
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+0
3
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| 1, 364, 132131, 47963189, 17410505476, 6319965524599, 2294130074923961, 832762897231873244, 302290637565095063611, 109730668673232276217549, 39831930437745751171906676, 14458881018233034443125905839
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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(19*a(n))^2 - 365*b(n)^2 = -4 with b(n)=A098253(n) give all positive solutions of this Pell equation.
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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, 363) + S(n-1, 363) = S(2*n, sqrt(365)), with S(n, x)=U(n, x/2) Chebyshev's polynomials of the second kind, A049310. S(-1, x)= 0 = U(-1, x). S(n, 363)=A098251(n).
a(n)= (-2/19)*I*((-1)^n)*T(2*n+1, 19*I/2) with the imaginary unit I and Chebyshev's polynomials of the first kind. See the T-triangle A053120.
G.f.: (1+x)/(1-363*x+x^2).
a(n)=363*a(n-1)-a(n-2), n>1 ; a(0)=1, a(1)=364 . [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 18 2008]
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EXAMPLE
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All positive solutions of Pell equation x^2 - 365*y^2 = -4 are
(19=19*1,1), (6916=19*364,362), (2510489=19*132131,131405),
(911300591=19*47963189,47699653), ...
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CROSSREFS
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Sequence in context: A107509 A140935 A022196 this_sequence A099113 A073304 A011763
Adjacent sequences: A098249 A098250 A098251 this_sequence A098253 A098254 A098255
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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), Sep 10 2004
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