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A077409
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Bisection (even part) of Chebyshev sequence with Diophantine property.
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5
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7, 59, 583, 5771, 57127, 565499, 5597863, 55413131, 548533447, 5429921339, 53750679943, 532076878091, 5267018100967, 52138104131579, 516114023214823, 5109002128016651, 50573907256951687, 500630070441500219, 4955726797158050503, 49056637901139004811
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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COMMENTS
| a(n)^2 - 24*b(n)^2 = 25, with the companion sequence b(n)= A077251(n).
The odd part is A077250(n) with Diophantine companion A077249(n).
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LINKS
| Index to sequences with linear recurrences with constant coefficients, signature (10,-1).
Tanya Khovanova, Recursive Sequences
Index entries for sequences related to Chebyshev polynomials.
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FORMULA
| a(n)= 10*a(n-1)- a(n-2), a(-1) := 11, a(0)=7.
a(n)= T(n+1, 5)+2*T(n, 5), with T(n, x) Chebyshev's polynomials of the first kind, A053120. T(n, 5)=A001079(n).
a(n) = sqrt(24*A077251(n)^2 + 25).
G.f.: (7-11*x)/(1-10*x+x^2).
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EXAMPLE
| 59 = a(1) = sqrt(24*A077251(1)^2 + 25) = sqrt(24*12^2 + 25) = sqrt(3481) = 59.
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MATHEMATICA
| CoefficientList[Series[(7 - 11 z)/(z^2 - 10 z + 1), {z, 0, 200}], z] (* From Vladimir Joseph Stephan Orlovsky, Jun 11 2011 *)
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PROG
| (PARI) a(n)=if(n<0, 0, subst(poltchebi(n+1)+2*poltchebi(n), x, 5))
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CROSSREFS
| Sequence in context: A101487 A099659 A135150 * A192458 A203237 A099347
Adjacent sequences: A077406 A077407 A077408 * A077410 A077411 A077412
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KEYWORD
| nonn,easy
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AUTHOR
| Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), Nov 08, 2002
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