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A077249 Bisection (odd part) of Chebyshev sequence with Diophantine property. 6
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; text; internal format)
OFFSET

0,1

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).

LINKS

Colin Barker, Table of n, a(n) for n = 0..1000

Tanya Khovanova, Recursive Sequences

Index entries for sequences related to Chebyshev polynomials.

Index entries for linear recurrences with constant coefficients, signature (10,-1).

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).

EXAMPLE

24*a(1)^2 + 25 = 24*21^2+25 = 10609 = 103^2 = A077250(1)^2.

MATHEMATICA

CoefficientList[Series[(z + 2)/(z^2 - 10 z + 1), {z, 0, 200}], z] (* Vladimir Joseph Stephan Orlovsky, Jun 11 2011 *)

LinearRecurrence[{10, -1}, {2, 21}, 40] (* Harvey P. Dale, Apr 08 2012 *)

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

(PARI) Vec((2+x)/(1-10*x+x^2) + O(x^30)) \\ Colin Barker, Jun 15 2015

CROSSREFS

Sequence in context: A037644 A110253 A185634 * A068070 A085953 A225614

Adjacent sequences:  A077246 A077247 A077248 * A077250 A077251 A077252

KEYWORD

nonn,easy

AUTHOR

Wolfdieter Lang, Nov 08 2002

STATUS

approved

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Last modified March 26 23:19 EDT 2017. Contains 284141 sequences.