This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A118576 #17 Mar 16 2024 14:24:29
%S A118576 0,2145,3773,6468,8540,12005,19208,24521,28665,35672,41148,50421,
%T A118576 61388,69972,84525,95921,115248,156065,186480,210308,250733,282405,
%U A118576 336140,399797,449673,534296,600600,713097,950796,1127973,1266797,1502340
%N A118576 Nonnegative values x of solutions (x, y) to the Diophantine equation x^2+(x+16807)^2 = y^2.
%C A118576 Also values x of Pythagorean triples (x, x+16807, y); 16807 = 7^5.
%C A118576 Corresponding values y of solutions (x, y) are in A156713.
%C A118576 Limit_{n -> oo} a(n)/a(n-11) = 3+2*sqrt(2).
%C A118576 Limit_{n -> oo} a(n)/a(n-1) = ((9+4*sqrt(2))/7)^5 / (3+2*sqrt(2))^2 for n mod 11 = {1, 2, 4, 6, 8, 10}.
%C A118576 Limit_{n -> oo} a(n)/a(n-1) = (3+2*sqrt(2))^3 / ((9+4*sqrt(2))/7)^7 for n mod 11 = {0, 3, 5, 9}.
%C A118576 Limit_{n -> oo} a(n)/a(n-1) = (3+2*sqrt(2)) / ((9+4*sqrt(2))/7)^2 for n mod 11 = 7.
%H A118576 <a href="/index/Rec#order_23">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,0,0,0,0,0,0,6,-6,0,0,0,0,0,0,0,0,0,-1,1).
%F A118576 a(n) = 6*a(n-11)-a(n-22)+33614 for n > 22; a(1) = 0, a(2) = 2145, a(3) = 3773, a(4) = 6468, a(5) = 8540, a(6) = 12005, a(7) = 19208, a(8) = 24521, a(9) = 28665, a(10) = 35672, a(11) = 41148, a(12) = 50421, a(13) = 61388, a(14) = 69972, a(15) = 84525, a(16) = 95921, a(17) = 115248, a(18) = 156065, a(19) = 186480, a(20) = 210308, a(21) = 250733, a(22) = 282405.
%F A118576 G.f.: x*(2145+1628*x+2695*x^2+2072*x^3+3465*x^4+7203*x^5+5313*x^6+4144*x^7+7007*x^8+5476*x^9+9273*x^10-1903*x^11-1184*x^12-1617*x^13-1036*x^14-1463*x^15-2401*x^16-1463*x^17 -1036*x^18-1617*x^19-1184*x^20-1903*x^21 )/((1-x)*(1-6*x^11+x^22)).
%o A118576 (PARI) {forstep(n=0, 1600000, [1, 3], if(issquare(2*n^2 + 33614*n + 282475249), print1(n, ",")))}
%Y A118576 Cf. A156713, A156035 (decimal expansion of 3+2*sqrt(2)), A156649 (decimal expansion of (9+4*sqrt(2))/7).
%K A118576 nonn,easy
%O A118576 1,2
%A A118576 _Mohamed Bouhamida_, May 16 2006
%E A118576 Edited by _Klaus Brockhaus_, Feb 14 2009