|
Search: id:A097728
|
|
|
| A097728 |
|
Chebyshev U(n,x) polynomial evaluated at x=73 = 2*6^2+1. |
|
+0
2
|
|
| 1, 146, 21315, 3111844, 454307909, 66325842870, 9683118751111, 1413669011819336, 206385992606871945, 30130941251591484634, 4398911036739749884619, 642210880422751891669740
(list; graph; listen)
|
|
|
OFFSET
|
0,2
|
|
|
COMMENT
|
Used to form integer solutions of Pell equation a^2 - 37*b^2 =-1. See A097729 with A097730.
|
|
LINKS
|
Tanya Khovanova, Recursive Sequences
Index entries for sequences related to Chebyshev polynomials.
|
|
FORMULA
|
a(n) = 2*73*a(n-1) - a(n-2), n>=1, a(0)=1, a(-1):=0.
a(n) = S(n, 2*73)= U(n, 73), Chebyshev's polynomials of the second kind. See A049310.
G.f.: 1/(1-146*x+x^2).
a(n)= sum((-1)^k*binomial(n-k, k)*146^(n-2*k), k=0..floor(n/2)), n>=0.
a(n) = ((73+12*sqrt(37))^(n+1) - (73-12*sqrt(37))^(n+1))/(24*sqrt(37)).
|
|
CROSSREFS
|
Sequence in context: A158132 A043431 A166219 this_sequence A145212 A122064 A162701
Adjacent sequences: A097725 A097726 A097727 this_sequence A097729 A097730 A097731
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
Wolfdieter Lang (wolfdieter.lang_AT_physik_DOT_uni-karlsruhe_DOT_de), Aug 31 2004
|
|
|
Search completed in 0.002 seconds
|
