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 A124100 #28 May 25 2025 16:56:37
%S A124100 1,40,1089,25160,531521,10625640,204744769,3844391560,70827391041,
%T A124100 1286290883240,23101397290049,411249127989960,7269184506192961,
%U A124100 127745926316548840,2234231991096868929,38920247688751940360
%N A124100 Sum_(x^i*y^j*z^k) with i + j + k = m and (x, y, z) = the primitive Pythagorean triple (8, 15, 17).
%D A124100 G. Balzarotti and P. P. Lava, Le sequenze di numeri interi, Hoepli, 2008, p. 196.
%H A124100 Harvey P. Dale, <a href="/A124100/b124100.txt">Table of n, a(n) for n = 0..811</a>
%H A124100 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (40, -511, 2040).
%F A124100 a(m) = (x^(m+2)*(z-y) + y^(m+2)*(x-z) + z^(m+2)*(y-x))/((x-y)*(y-z)*(z-x)).
%F A124100 From _Chai Wah Wu_, Sep 24 2016: (Start)
%F A124100 a(n) = 40*a(n-1) - 511*a(n-2) + 2040*a(n-3) for n > 2.
%F A124100 G.f.: 1/((1 - 8*x)*(1 - 15*x)*(1 - 17*x)). (End)
%F A124100 a(n) = 2^(3*n+6)/63 - 15^(n+2)/14 + 17^(n+2)/18. - _Vaclav Kotesovec_, Sep 25 2016
%e A124100 a(2) = 1089 because x^2 + y^2 + z^2 + x*y + x*z + y*z = 8^2 + 15^2 + 17^2 + 8*15 + 8*17 + 15*17 = 1089 and x^2 + y^2 = z^2.
%p A124100 seq(sum(8^(m-n)*sum(15^p*17^(n-p),p=0..n),n=0..m),m=0..N);
%t A124100 LinearRecurrence[{40,-511,2040},{1,40,1089},30] (* _Harvey P. Dale_, May 25 2025 *)
%Y A124100 Cf. A019682, A020000, A020340-A020342, A020344-A020346, A021664, A021684, A021844, A025942, A077515.
%K A124100 nonn
%O A124100 0,2
%A A124100 _Giorgio Balzarotti_ and _Paolo P. Lava_, Nov 26 2006