1,2

Also values x of Pythagorean triples (x, x+2401, y); 2401=7^4.

Corresponding values y of solutions (x, y) are in A157247.

lim_{n -> infinity} a(n)/a(n-9) = 3+2*sqrt(2).

lim_{n -> infinity} a(n)/a(n-1) = (3+2*sqrt(2)) / ((9+4*sqrt(2))/7)^2 for n mod 9 = {1, 2, 6}.

lim_{n -> infinity} a(n)/a(n-1) = ((9+4*sqrt(2))/7)^5 / (3+2*sqrt(2))^2 for n mod 9 = {0, 3, 5, 7}.

lim_{n -> infinity} a(n)/a(n-1) = (3+2*sqrt(2))^3 / ((9+4*sqrt(2))/7)^7 for n mod 9 = {4, 8}.

a(n)=6*a(n-9)-a(n-18)+4802 for n > 18; a(1)=0, a(2)=539, a(3)=924, a(4)=1220, a(5)=1715, a(6)=2744, a(7)=3503, a(8)=4095, a(9)=5096, a(10)=7203, a(11)=9996, a(12)=12075, a(13)=13703, a(14)=16464,a (15)=22295, a(16)=26640, a(17)=30044, a(18)=35819.

G.f.: x*(539+385*x+296*x^2+495*x^3+1029*x^4+759*x^5+592*x^6 +1001*x^7+2107*x^8-441*x^9-231*x^10-148*x^11-209*x^12-343*x^13 -209*x^14-148*x^15-231*x^16-441*x^17) / ((1-x)*(1-6*x^9+x^18)).

a(9*k+1) = 2401*A001652(k) for k >= 0.

924^2+(924+2401)^2 = 853776+11055625 = 11909401 = 3451^2.

(PARI) {forstep(n=0, 1100000, [3 , 1], if(issquare(n^2+(n+2401)^2), print1(n, ", ")))}

Cf. A157247, A001652, A118576, A118554, A118611, A156035 (decimal expansion of 3+2*sqrt(2)), A156649 (decimal expansion of (9+4*sqrt(2))/7).

Sequence in context: A077076 A033916 A111258 this_sequence A146123 A159207 A101705

Adjacent sequences: A118627 A118628 A118629 this_sequence A118631 A118632 A118633

nonn

Mohamed Bouhamida (bhmd95(AT)yahoo.fr), May 09 2006

Edited by Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Feb 25 2009