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 A226028 #17 Feb 16 2025 08:33:19
%S A226028 3,22,17,49,103,43,69,217,244,81,156,305,505,445,131,187,671,709,913,
%T A226028 706,193,190,793,1546,1281,1441,1027,267,295,799,1819,2781,2021,2089,
%U A226028 1408,353,465,1249,1828,3265,4376,2929,2857,1849,451,498,1937,2863,3277,5131,6331,4005,3745,2350,561
%N A226028 Array T(j,k) of counts of internal lattice points within all Pythagorean triangles (see comments for array order).
%C A226028 The array of counts of internal lattice points within all Pythagorean triangles T(j,k) is arranged so that its first column is the ordered counts of internal lattice points within the k-th primitive Pythagorean triangle (PPT) A225414(k) and the j-th column is j multiples of these PPT side lengths.
%C A226028 Let the k-th PPT have integer perpendicular sides a, b then its j-th multiple has area A = j^2*a*b/2 and the count of lattice points intersected by its boundary is B = j*(a+b+1) by the application of Pick's theorem the count of internal lattice points within it is I = (j^2*a*b-j*(a+b+1)+2)/2.
%H A226028 Eric W. Weisstein, <a href="https://mathworld.wolfram.com/PicksTheorem.html">MathWorld: Pick's Theorem</a>
%H A226028 Wikipedia, <a href="http://en.wikipedia.org/wiki/Pick%27s_theorem">Pick's theorem</a>
%e A226028 Array begins
%e A226028 3, 17, 43, 81, 131, ...
%e A226028 22, 103, 244, 445, ...
%e A226028 49, 217, 505, ...
%e A226028 69, 305, ...
%e A226028 156, ...
%t A226028 getpairs[k_] := Reverse[Select[IntegerPartitions[k, {2}], GCD[#[[1]], #[[2]]]==1 &]]; getpptpairs[j_] := (newlist=getpairs[j]; Table[{(newlist[[m]][[1]]^2-newlist[[m]][[2]]^2-1)(2newlist[[m]][[1]]*newlist[[m]][[2]]-1)/2, newlist[[m]][[1]]^2-newlist[[m]][[2]]^2, 2newlist[[m]][[1]]*newlist[[m]][[2]]}, {m, 1, Length[newlist]}]); lexicographicLattice[{dim_, maxHeight_}] := Flatten[Array[Sort@Flatten[(Permutations[#1] &) /@ IntegerPartitions[#1 +dim-1, {dim}], 1] &, maxHeight], 1]; array[{x_, y_}] := (pptpair=table[[y]]; (x^2*pptpair[[2]]*pptpair[[3]])/2-x(pptpair[[2]]+pptpair[[3]]+1)/2+1); maxterms=20; table=Sort[Flatten[Table[getpptpairs[2p+1], {p, 1, maxterms}], 1]][[1;;maxterms]]; pairs=lexicographicLattice[{2, maxterms}]; Table[array[pairs[[n]]], {n, 1, maxterms(maxterms+1)/2}]
%Y A226028 Cf. A126587 (first row), A225414 (first column).
%K A226028 nonn,tabl
%O A226028 1,1
%A A226028 _Frank M Jackson_, May 23 2013