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A077251 Bisection (even part) of Chebyshev sequence with Diophantine property. +0
5
1, 12, 119, 1178, 11661, 115432, 1142659, 11311158, 111968921, 1108378052, 10971811599, 108609737938, 1075125567781, 10642645939872, 105351333830939, 1042870692369518, 10323355589864241, 102190685206272892 (list; graph; listen)
OFFSET

0,2

COMMENT

b(n)^2 - 24*a(n)^2 = 25, with the companion sequence b(n)= A077409(n).

The odd part is A077249(n) with Diophantine companion A077250(n).

LINKS

Index entries for sequences related to linear recurrences with constant coefficients

Tanya Khovanova, Recursive Sequences

Index entries for sequences related to Chebyshev polynomials.

FORMULA

a(n)= 10*a(n-1)- a(n-2), a(-1) := -2, a(0)=1.

a(n)= S(n, 10)+2*S(n-1, 10), with S(n, x) := U(n, x/2), Chebyshev's polynomials of the 2nd kind, A049310. S(n, 10)= A004189(n+1).

a(n)= sqrt((A077409(n)^2 - 25)/24).

G.f.: (1+2*x)/(1-10*x+x^2).

EXAMPLE

24*a(1)^2 + 25 = 24*12^2 + 25 = 3481 = 59^2 = A077409(1)^2.

CROSSREFS

Sequence in context: A163950 A025132 A001712 this_sequence A075622 A153054 A075366

Adjacent sequences: A077248 A077249 A077250 this_sequence A077252 A077253 A077254

KEYWORD

nonn,easy

AUTHOR

Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), Nov 08 2002

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Last modified December 13 23:45 EST 2009. Contains 170824 sequences.


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