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 A124099 #26 Jul 03 2023 08:20:38 %S A124099 1,30,619,10920,177061,2726130,40547359,588485820,8387148121, %T A124099 117876868230,1638536364499,22574666496720,308755233696781, %U A124099 4197234089634330,56765041887676039,764357559726523620 %N A124099 Sum_(x^i*y^j*z^k) with i + j + k = m and (x, y, z) = the primitive Pythagorean triple (5, 12, 13). %D A124099 G. Balzarotti and P. P. Lava, Le sequenze di numeri interi, Hoepli, 2008, p. 196. %H A124099 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (30, -281, 780). %F A124099 a(m) = (x^(m+2)*(z-y)+y^(m+2)*(x-z)+z^(m+2)*(y-x))/((x-y)*(y-z)*(z-x)). %F A124099 From _Chai Wah Wu_, Sep 24 2016: (Start) %F A124099 a(n) = 30*a(n-1) - 281*a(n-2) + 780*a(n-3) for n > 2. %F A124099 G.f.: 1/((1 - 5*x)*(1 - 12*x)*(1 - 13*x)). (End) %e A124099 a(2)=619 because Sum_(x^i*y^j*z^k) = x^2 + y^2 + z^2 + x*y + x*z + y*z = 5^2 + 12^2 + 13^2 + 5*12 + 5*13 + 12*13 = 619 and x^2 + y^2 = z^2. %p A124099 seq(sum(5^(m-n)*sum(12^p*13^(n-p),p=0..n),n=0..m),m=0..N); %Y A124099 Cf. A019682, A020000, A020341, A020346, A021664, A021684, A021844, A025942. %K A124099 nonn %O A124099 0,2 %A A124099 _Giorgio Balzarotti_ and _Paolo P. Lava_, Nov 26 2006