This site is supported by donations to The OEIS Foundation.

The OEIS is looking to hire part-time people to help edit core sequences, upload scanned documents, process citations, fix broken links, etc. - Neil Sloane, njasloane@gmail.com

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A098255 Chebyshev polynomials S(n,443) + S(n-1,443) with Diophantine property. 3
 1, 444, 196691, 87133669, 38600018676, 17099721139799, 7575137864912281, 3355768974435000684, 1486598080536840390731, 658559593908845858093149, 291740413503538178294874276, 129240344622473504138771211119 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS (21*a(n))^2 - 445*b(n)^2 = -4 with b(n)=A098256(n) give all positive solutions of this Pell equation. LINKS Indranil Ghosh, Table of n, a(n) for n = 0..377 Tanya Khovanova, Recursive Sequences Index entries for linear recurrences with constant coefficients, signature (443, -1). FORMULA a(n) = S(n, 443) + S(n-1, 443) = S(2*n, sqrt(445)), with S(n, x)=U(n, x/2) Chebyshev's polynomials of the second kind, A049310. S(-1, x)= 0 = U(-1, x). S(n, 443)=A098254(n). a(n) = (-2/21)*I*((-1)^n)*T(2*n+1, 21*I/2) with the imaginary unit I and Chebyshev's polynomials of the first kind. See the T-triangle A053120. G.f.: (1+x)/(1-443*x+x^2). a(n) = 443*a(n-1)-a(n-2), n>1 ; a(0)=1, a(1)=444 . [Philippe Deléham, Nov 18 2008] EXAMPLE All positive solutions of Pell equation x^2 - 445*y^2 = -4 are (21=21*1,1), (9324=21*444,442), (4130511=21*196691,195805),(1829807049=21*87133669,86741173), ... MATHEMATICA LinearRecurrence[{443, -1}, {1, 444}, 12] (* Indranil Ghosh, Feb 18 2017 *) CROSSREFS Sequence in context: A233711 A251294 A233377 * A028460 A105985 A160583 Adjacent sequences:  A098252 A098253 A098254 * A098256 A098257 A098258 KEYWORD nonn,easy AUTHOR Wolfdieter Lang, Sep 10 2004 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.