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A077249
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Bisection (odd part) of Chebyshev sequence with Diophantine property.
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5
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2, 21, 208, 2059, 20382, 201761, 1997228, 19770519, 195707962, 1937309101, 19177383048, 189836521379, 1879187830742, 18602041786041, 184141230029668, 1822810258510639, 18043961355076722, 178616803292256581, 1768124071567489088, 17502623912382634299
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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COMMENTS
| -24*a(n)^2 + b(n)^2 = 25, with the companion sequence b(n)= A077250(n).
The even part is A077251(n) with Diophantine companion A077409(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) := -1, a(0)=2.
a(n)= 2*S(n, 10)+S(n-1, 10), with S(n, x) := U(n, x/2), Chebyshev polynomials of 2nd kind, A049310. S(n, 10)= A004189(n+1).
G.f.: (2+x)/(1-10*x+x^2).
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EXAMPLE
| 24*a(1)^2 + 25 = 24*21^2+25 = 10609 = 103^2 = A077250(1)^2.
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MATHEMATICA
| CoefficientList[Series[(z + 2)/(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(-7*poltchebi(n)+11*poltchebi(n+1), x, 5)/24)
(PARI) a(n)=2*polchebyshev(n, 2, 5)+polchebyshev(n-1, 2, 5) \\ Charles R Greathouse IV, Jun 11 2011
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CROSSREFS
| Sequence in context: A037756 A037644 A110253 * A068070 A085953 A037527
Adjacent sequences: A077246 A077247 A077248 * A077250 A077251 A077252
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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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