|
| |
|
|
A097741
|
|
Pell equation solutions (10*a(n))^2 - 101*b(n)^2 = -1 with b(n):=A097742(n), n>=0.
|
|
2
| |
|
|
1, 403, 162005, 65125607, 26180332009, 10524428342011, 4230794013156413, 1700768668860536015, 683704774087922321617, 274847618414675912754019, 110488058897925629004794021, 44415924829347688184014442423
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,2
|
|
|
LINKS
| Tanya Khovanova, Recursive Sequences
Index entries for sequences related to Chebyshev polynomials.
|
|
|
FORMULA
| a(n)= S(n, 2*201) + S(n-1, 2*201) = S(2*n, 2*sqrt(101)), with Chebyshev polynomials of the 2nd kind. See A049310 for the triangle of S(n, x)= U(n, x/2) coefficients. S(-1, x) := 0 =: U(-1, x).
a(n)= ((-1)^n)*T(2*n+1, 10*I)/(10*I) with the imaginary unit I and Chebyshev polynomials of the first kind. See the T-triangle A053120.
G.f.: (1+x)/(1-2*201*x+x^2).
a(n)=402*a(n-1)-a(n-2), n>1 ; a(0)=1, a(1)=403 . [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 18 2008]
|
|
|
EXAMPLE
| (x,y) = (10*1=10;1), (4030=10*403;401), (1620050=10*162005;161201), ... give the positive integer solutions to x^2 - 101*y^2 =-1.
|
|
|
MATHEMATICA
| LinearRecurrence[{402, -1}, {1, 403}, 20] (* or *) CoefficientList[Series[ (1+x)/(1-402x+x^2), {x, 0, 20}], x] (* From Harvey P. Dale, Apr 20 2011 *)
|
|
|
CROSSREFS
| Cf. A097740 for S(n, 2*201).
Sequence in context: A097740 A083815 A165808 * A117836 A185640 A185637
Adjacent sequences: A097738 A097739 A097740 * A097742 A097743 A097744
|
|
|
KEYWORD
| nonn,easy
|
|
|
AUTHOR
| Wolfdieter Lang (wolfdieter.lang_AT_physik_DOT_uni-karlsruhe_DOT_de), Aug 31 2004
|
| |
|
|
