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!)
 A098252 Chebyshev polynomials S(n,363) + S(n-1,363) with Diophantine property. 3
 1, 364, 132131, 47963189, 17410505476, 6319965524599, 2294130074923961, 832762897231873244, 302290637565095063611, 109730668673232276217549, 39831930437745751171906676, 14458881018233034443125905839 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS (19*a(n))^2 - 365*b(n)^2 = -4 with b(n)=A098253(n) give all positive solutions of this Pell equation. LINKS Indranil Ghosh, Table of n, a(n) for n = 0..369 Tanya Khovanova, Recursive Sequences Index entries for linear recurrences with constant coefficients, signature (363,-1). FORMULA a(n)= S(n, 363) + S(n-1, 363) = S(2*n, sqrt(365)), 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, 363)=A098251(n). a(n)= (-2/19)*I*((-1)^n)*T(2*n+1, 19*I/2) with the imaginary unit I and Chebyshev's polynomials of the first kind. See the T-triangle A053120. G.f.: (1+x)/(1-363*x+x^2). a(n)=363*a(n-1)-a(n-2), n>1 ; a(0)=1, a(1)=364 . [From Philippe Deléham, Nov 18 2008] EXAMPLE All positive solutions of Pell equation x^2 - 365*y^2 = -4 are (19=19*1,1), (6916=19*364,362), (2510489=19*132131,131405), (911300591=19*47963189,47699653), ... MATHEMATICA LinearRecurrence[{363, -1}, {1, 364}, 20] (* Harvey P. Dale, Feb 03 2015 *) CROSSREFS Sequence in context: A140935 A249671 A022196 * A221393 A099113 A073304 Adjacent sequences:  A098249 A098250 A098251 * A098253 A098254 A098255 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.