|
Search: id:A097844
|
|
|
| A097844 |
|
Chebyshev polynomials S(n,171). |
|
+0
3
|
|
| 1, 171, 29240, 4999869, 854948359, 146191169520, 24997835039561, 4274483600595411, 730911697866775720, 124981625851618052709, 21371127108928820237519, 3654337754000976642563040
(list; graph; listen)
|
|
|
OFFSET
|
0,2
|
|
|
COMMENT
|
Used for all positive integer solutions of Pell equation x^2 - 173*y^2 = -4. See A097845 with A098244.
|
|
LINKS
|
Tanya Khovanova, Recursive Sequences
Index entries for sequences related to Chebyshev polynomials.
|
|
FORMULA
|
a(n)= S(n, 171)=U(n, 171/2)= S(2*n+1, sqrt(173))/sqrt(173) with S(n, x)=U(n, x/2) Chebyshev's polynomials of the second kind, A049310. S(-1, x)= 0 = U(-1, x).
a(n)=171*a(n-1)-a(n-2), n >= 1; a(0)=1, a(1)=171; a(-1):=0.
a(n)=(ap^(n+1) - am^(n+1))/(ap-am) with ap := (171+13*sqrt(173))/2 and am := (171-13*sqrt(173))/2 = 1/ap.
G.f.: 1/(1-171*x+x^2).
|
|
CROSSREFS
|
Adjacent sequences: A097841 A097842 A097843 this_sequence A097845 A097846 A097847
Sequence in context: A016058 A127959 A046166 this_sequence A076573 A015356 A067356
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
Wolfdieter Lang (wolfdieter.lang_AT_physik_DOT_uni-karlsruhe_DOT_de), Sep 10 2004
|
|
|
Search completed in 0.002 seconds
|
