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Search: id:A077420
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| A077420 |
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Bisection of Chebyshev sequence T(n,3) (odd part) with Diophantine property. |
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6
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| 1, 33, 1121, 38081, 1293633, 43945441, 1492851361, 50713000833, 1722749176961, 58522759015841, 1988051057361633, 67535213191279681, 2294209197446147521, 77935577499977736033, 2647515425801796877601
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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(3*a(n))^2 - 2*(2*b(n))^2 = 1 with companion sequence b(n)= A046176(n+1), n>=0 (special solutions of 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) = 34*a(n-1) - a(n-2), a(-1)=1, a(0)=1.
a(n) = T(2*n+1, 3)/3 = S(n, 34) - S(n-1, 34) with S(n, x) := U(n, x/2), resp. T(n, x), Chebyshev's polynomials of the second, resp. first, kind. See A049310 and A053120. S(-1, x)=0, S(n, 34)= A029547(n), T(n, 3)=A001541(n).
G.f.: (1-x)/(1-34*x+x^2).
a(n)= sqrt(8*A046176(n+1)^2 + 1)/3.
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CROSSREFS
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Cf. A056771 (even part).
Row 34 of array A094954.
Sequence in context: A132469 A009977 A130835 this_sequence A158688 A065424 A071268
Adjacent sequences: A077417 A077418 A077419 this_sequence A077421 A077422 A077423
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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 29 2002
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