|
Search: id:A078989
|
|
|
| A078989 |
|
Chebyshev sequence with Diophantine property. |
|
+0
5
|
|
| 1, 67, 4421, 291719, 19249033, 1270144459, 83810285261, 5530208682767, 364909962777361, 24078527334623059, 1588817894122344533, 104837902484740116119, 6917712746098725319321, 456464203340031130959067
(list; graph; listen)
|
|
|
OFFSET
|
0,2
|
|
|
COMMENT
|
One fourth of bisection (even part) of A041024.
(4*a(n))^2 - 17*A078988(n)^2= -1 (Pell -1 equation, see A077232-3).
|
|
LINKS
|
Tanya Khovanova, Recursive Sequences
Index entries for sequences related to Chebyshev polynomials.
|
|
FORMULA
|
a(n)= 66*a(n-1) - a(n-2), n>=1, a(-1)=-1, a(0)=1.
G.f.: (1+x)/(1-66*x+x^2).
a(n)= S(2*n, 2*sqrt(17)) = -i*((-1)^n)*T(2*n+1, 4*i)/4 = S(n, 66) + S(n-1, 66) with i^2=-1 and S(n, x), resp. T(n, x), Chebyshev's polynomials of the second, resp. first, kind. See A049310 and A053120.
a(n)=A041024(2*n)/4.
|
|
EXAMPLE
|
(x,y) = (4,1), (268,65), (17684,4289), ... give the positive integer solutions to x^2 - 17*y^2 =-1.
|
|
CROSSREFS
|
Cf. A097316 for S(n, 66).
Sequence in context: A069397 A103727 A120663 this_sequence A156121 A144940 A087536
Adjacent sequences: A078986 A078987 A078988 this_sequence A078990 A078991 A078992
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), Jan 10 2003
|
|
|
Search completed in 0.005 seconds
|
