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 A129642 Nonnegative values x of solutions (x, y) to the Diophantine equation x^2+(x+457)^2 = y^2. 6
 0, 348, 495, 1371, 3255, 4088, 9140, 20096, 24947, 54383, 118235, 146508, 318072, 690228, 855015, 1854963, 4024047, 4984496, 10812620, 23454968, 29052875, 63021671, 136706675, 169333668, 367318320, 796785996, 986950047, 2140889163 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Also values x of Pythagorean triples (x, x+457, y). Corresponding values y of solutions (x, y) are in A160580. lim_{n -> infinity} a(n)/a(n-3) = 3+2*sqrt(2). lim_{n -> infinity} a(n)/a(n-1) = (601+276*sqrt(2))/457 for n mod 3 = {1, 2}. lim_{n -> infinity} a(n)/a(n-1) = (213651+31850*sqrt(2))/457^2 for n mod 3 = 0. LINKS Harvey P. Dale, Table of n, a(n) for n = 1..1000 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)+914 for n > 6; a(1)=0, a(2)=348, a(3)=495, a(4)=1371, a(5)=3255, a(6)=4088. G.f.: x*(348+147*x+876*x^2-204*x^3-49*x^4-204*x^5)/((1-x)*(1-6*x^3+x^6)). a(3*k+1) = 457*A001652(k) for k >= 0. a(1)=0, a(2)=348, a(3)=495, a(4)=1371, a(5)=3255, a(6)=4088, a(7)=9140, a(n)=a(n-1)+6*a(n-3)-6*a(n-4)-a(n-6)+a(n-7) [From Harvey P. Dale, May 13 2012] MATHEMATICA LinearRecurrence[{1, 0, 6, -6, 0, -1, 1}, {0, 348, 495, 1371, 3255, 4088, 9140}, 30] (* Harvey P. Dale, May 13 2012 *) PROG (PARI) {forstep(n=0, 10000000, [3, 1], if(issquare(2*n^2+914*n+208849), print1(n, ", ")))} CROSSREFS Cf. A160580, A001652, A129641, A156035 (decimal expansion of 3+2*sqrt(2)), A160581 (decimal expansion of (601+276*sqrt(2))/457), A160582 (decimal expansion of (213651+31850*sqrt(2))/457^2). Sequence in context: A323999 A293512 A275237 * A304837 A231089 A237318 Adjacent sequences:  A129639 A129640 A129641 * A129643 A129644 A129645 KEYWORD nonn,easy AUTHOR Mohamed Bouhamida (bhmd95(AT)yahoo.fr), May 31 2007 EXTENSIONS Edited and two terms added by Klaus Brockhaus, Jun 08 2009 STATUS approved

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Last modified December 9 22:27 EST 2019. Contains 329880 sequences. (Running on oeis4.)