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Search: id:A077251
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| A077251 |
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Bisection (even part) of Chebyshev sequence with Diophantine property. |
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+0
5
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| 1, 12, 119, 1178, 11661, 115432, 1142659, 11311158, 111968921, 1108378052, 10971811599, 108609737938, 1075125567781, 10642645939872, 105351333830939, 1042870692369518, 10323355589864241, 102190685206272892
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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b(n)^2 - 24*a(n)^2 = 25, with the companion sequence b(n)= A077409(n).
The odd part is A077249(n) with Diophantine companion A077250(n).
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LINKS
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Index entries for sequences related to linear recurrences with constant coefficients
Tanya Khovanova, Recursive Sequences
Index entries for sequences related to Chebyshev polynomials.
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FORMULA
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a(n)= 10*a(n-1)- a(n-2), a(-1) := -2, a(0)=1.
a(n)= S(n, 10)+2*S(n-1, 10), with S(n, x) := U(n, x/2), Chebyshev's polynomials of the 2nd kind, A049310. S(n, 10)= A004189(n+1).
a(n)= sqrt((A077409(n)^2 - 25)/24).
G.f.: (1+2*x)/(1-10*x+x^2).
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EXAMPLE
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24*a(1)^2 + 25 = 24*12^2 + 25 = 3481 = 59^2 = A077409(1)^2.
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CROSSREFS
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Sequence in context: A163950 A025132 A001712 this_sequence A075622 A153054 A075366
Adjacent sequences: A077248 A077249 A077250 this_sequence A077252 A077253 A077254
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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.uni-karlsruhe.de), Nov 08 2002
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