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 A129837 Nonnegative values x of solutions (x, y) to the Diophantine equation x^2+(x+119)^2 = y^2. 4
 0, 24, 49, 57, 85, 136, 180, 196, 261, 357, 481, 616, 660, 816, 1105, 1357, 1449, 1824, 2380, 3100, 3885, 4141, 5049, 6732, 8200, 8736, 10921, 14161, 18357, 22932, 24424, 29716, 39525, 48081, 51205, 63940, 82824, 107280, 133945, 142641, 173485, 230656 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Also values x of Pythagorean triples (x, x+119, y). Corresponding values y of solutions (x, y) are in A156650. lim_{n -> infinity} a(n)/a(n-9) = 3+2*sqrt(2). lim_{n -> infinity} a(n)/a(n-1) = ((9+4*sqrt(2))/7)/((19+6*sqrt(2))/17) for n mod 9 = {1, 2}. lim_{n -> infinity} a(n)/a(n-1) = ((19+6*sqrt(2))/17)^2/((9+4*sqrt(2))/7) for n mod 9 = {0, 3}. lim_{n -> infinity} a(n)/a(n-1) = (3+2*sqrt(2))/(((9+4*sqrt(2))/7)*((19+6*sqrt(2))/17)^2) for n mod 9 = {4, 8}. lim_{n -> infinity} a(n)/a(n-1) = ((9+4*sqrt(2))/7)^2*((19+6*sqrt(2))/17)/(3+2*sqrt(2)) for n mod 9 = {5, 7}. lim_{n -> infinity} a(n)/a(n-1) = (3+2*sqrt(2))/((9+4*sqrt(2))/7)^2 for n mod 9 = 6. LINKS FORMULA a(n) = 6*a(n-9)-a(n-18)+238 for n > 18; a(1)=0, a(2)=24, a(3)=49, a(4)=57, a(5)=85, a(6)=136, a(7)=180, a(8)=196, a(9)=261, a(10)=357, a(11)=481, a(12)=616, a(13)=660, a(14)=816, a(15)=1105, a(16)=1357, a(17)=1449, a(18)=1824. G.f.: x*(24+25*x+8*x^2+28*x^3+51*x^4+44*x^5+16*x^6+65*x^7+96*x^8-20*x^9-15*x^10-4*x^11-12*x^12-17*x^13-12*x^14-4*x^15-15*x^16-20*x^17 )/((1-x)*(1-6*x^9+x^18)) MATHEMATICA LinearRecurrence[{1, 0, 0, 0, 0, 0, 0, 0, 6, -6, 0, 0, 0, 0, 0, 0, 0, -1, 1}, {0, 24, 49, 57, 85, 136, 180, 196, 261, 357, 481, 616, 660, 816, 1105, 1357, 1449, 1824, 2380}, 140] (* From Vladimir Joseph Stephan Orlovsky, Feb 07 2012 *) PROG (PARI) {forstep(n=0, 240000, [1, 3], if(issquare(n^2+(n+119)^2), print1(n, ", ")))} CROSSREFS Cf. A156650, A156035 (decimal expansion of 3+2*sqrt(2)), A156649 (decimal expansion of (9+4*sqrt(2))/7), A156163 (decimal expansion of (19+6*sqrt(2))/17), A118630. Sequence in context: A073763 A030021 A105844 * A042140 A042138 A042136 Adjacent sequences:  A129834 A129835 A129836 * A129838 A129839 A129840 KEYWORD nonn AUTHOR Mohamed Bouhamida (bhmd95(AT)yahoo.fr), May 21 2007 EXTENSIONS Edited and extended by Klaus Brockhaus, Feb 13 2009 STATUS approved

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