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Search: id:A077239
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| A077239 |
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Bisection (odd part) of Chebyshev sequence with diophantine property. |
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+0
5
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| 7, 37, 215, 1253, 7303, 42565, 248087, 1445957, 8427655, 49119973, 286292183, 1668633125, 9725506567, 56684406277, 330380931095, 1925601180293, 11223226150663, 65413755723685, 381259308191447, 2222142093424997
(list; graph; listen)
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OFFSET
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0,1
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COMMENT
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a(n)^2 - 8*b(n)^2 = 17, with the companion sequence b(n)= A077413(n).
The even part is A077240(n) with diophantine companion A054488(n).
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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)= 6*a(n-1) - a(n-2), a(-1) := 5, a(0)=7.
a(n)= 2*T(n+1, 3)+T(n, 3), with T(n, x) Chebyshev's polynomials of the first kind, A053120. T(n, 3)= A001541(n).
G.f.: (7-5*x)/(1-6*x+x^2).
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EXAMPLE
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37 = a(1) = sqrt(8*A077413(1)^2 +17) = sqrt(8*13^2 + 17)= sqrt(1369) = 37.
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CROSSREFS
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Cf. A077242 (even and odd parts).
Sequence in context: A124610 A002683 A126475 this_sequence A046235 A025012 A039938
Adjacent sequences: A077236 A077237 A077238 this_sequence A077240 A077241 A077242
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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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