The OEIS is supported by the many generous donors to the OEIS Foundation.

 Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 59th year, we have over 358,000 sequences, and we’ve crossed 10,300 citations (which often say “discovered thanks to the OEIS”). Other ways to Give
 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A161486 Nonnegative values x of solutions (x, y) to the Diophantine equation x^2+(x+191)^2 = y^2. 4
 0, 69, 336, 573, 936, 2449, 3820, 5929, 14740, 22729, 35020, 86373, 132936, 204573, 503880, 775269, 1192800, 2937289, 4519060, 6952609, 17120236, 26339473, 40523236, 99784509, 153518160, 236187189, 581587200, 894769869, 1376600280 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Corresponding values y of solutions (x, y) are in A161487. lim_{n -> infinity} a(n)/a(n-3) = 3+2*sqrt(2). lim_{n -> infinity} a(n)/a(n-1) = (209+60*sqrt(2))/191 for n mod 3 = {1, 2}. lim_{n -> infinity} a(n)/a(n-1) = (52323+26522*sqrt(2))/191^2 for n mod 3 = 0. LINKS Index entries for linear recurrences with constant coefficients, signature (1,0,6,-6,0,-1,1). FORMULA a(n) = 6*a(n-3)-a(n-6)+382 for n > 6; a(1)=0, a(2)=69, a(3)=336, a(4)=573, a(5)=936, a(6)=2449. G.f.: x*(69+267*x+237*x^2-51*x^3-89*x^4-51*x^5) / ((1-x)*(1-6*x^3+x^6)). a(3*k+1) = 191*A001652(k) for k >= 0. MATHEMATICA Transpose[NestList[Flatten[{Rest[#], 6#[[4]]-First[#]+382}]&, {0, 69, 336, 573, 936, 2449}, 40]][[1]] (* Harvey P. Dale, Apr 01 2011 *) LinearRecurrence[{1, 0, 6, -6, 0, -1, 1}, {0, 69, 336, 573, 936, 2449, 3820}, 40] (* Harvey P. Dale, Mar 29 2016 *) PROG (PARI) {forstep(n=0, 10000000, [1, 3], if(issquare(2*n^2+382*n+36481), print1(n, ", ")))} CROSSREFS Cf. A161487, A001652, A156035 (decimal expansion of 3+2*sqrt(2)), A161488 (decimal expansion of (209+60*sqrt(2))/191), A161489 (decimal expansion of (52323+26522*sqrt(2))/191^2). Sequence in context: A069216 A158736 A262456 * A236158 A253342 A253335 Adjacent sequences: A161483 A161484 A161485 * A161487 A161488 A161489 KEYWORD nonn AUTHOR Klaus Brockhaus, Jun 13 2009 STATUS approved

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

Last modified December 6 11:26 EST 2022. Contains 358631 sequences. (Running on oeis4.)