|
| |
|
|
A077251
|
|
Bisection (even part) of Chebyshev sequence with Diophantine property.
|
|
5
|
|
|
|
1, 12, 119, 1178, 11661, 115432, 1142659, 11311158, 111968921, 1108378052, 10971811599, 108609737938, 1075125567781, 10642645939872, 105351333830939, 1042870692369518, 10323355589864241, 102190685206272892, 1011583496472864679, 10013644279522373898
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
0,2
|
|
|
COMMENTS
|
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
|
Table of n, a(n) for n=0..19.
Index to sequences with linear recurrences with constant coefficients, signature (10,-1).
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.
|
|
|
MATHEMATICA
|
CoefficientList[Series[(2 z + 1)/(z^2 - 10 z + 1), {z, 0, 200}], z] (* From Vladimir Joseph Stephan Orlovsky, Jun 11 2011 *)
|
|
|
PROG
|
(PARI) Vec((1+2*x)/(1-10*x+x^2)+O(x^99)) \\ Charles R Greathouse IV, Jun 11 2011
|
|
|
CROSSREFS
|
Sequence in context: A163950 A025132 A001712 * A075622 A153054 A075366
Adjacent sequences: A077248 A077249 A077250 * A077252 A077253 A077254
|
|
|
KEYWORD
|
nonn,easy,changed
|
|
|
AUTHOR
|
Wolfdieter Lang, Nov 08 2002
|
|
|
STATUS
|
approved
|
| |
|
|
