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 A135839 #25 Jul 25 2025 19:03:00
%S A135839 1,1,1,1,0,1,1,1,0,1,1,0,1,0,1,1,1,0,1,0,1,1,0,1,0,1,0,1,1,1,0,1,0,1,
%T A135839 0,1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,1,
%U A135839 0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1
%N A135839 Triangle read by rows: starting with A128174, replace left border with (1, 1, 1, ...).
%C A135839 Row sums = (1, 2, 2, 3, 3, 4, 4, 5, 5, ...).
%H A135839 Zhuorui He, <a href="/A135839/b135839.txt">Rows 1..150 of the triangle, flattened</a> (first 50 rows from G. C. Greubel)
%F A135839 Given A128174, replace left border with (1, 1, 1, ...). Triangle read by rows, odd rows = n terms of (1, 0, 1, ...); even rows = n terms of (1, 1, 0, 1, 0, 1, ...). By columns, leftmost column = (1, 1, 1, ...); all others = (1, 0, 1, 0, 1, ...).
%F A135839 T(n,1) = T(n,n) = 1, T(n,k) = (1 - (-1)^(n-k-1))/2. - _G. C. Greubel_,Dec 05 2016
%e A135839 First few rows of the triangle are:
%e A135839 1;
%e A135839 1, 1;
%e A135839 1, 0, 1;
%e A135839 1, 1, 0, 1;
%e A135839 1, 0, 1, 0, 1;
%e A135839 1, 1, 0, 1, 0, 1;
%e A135839 1, 0, 1, 0, 1, 0, 1;
%e A135839 ...
%t A135839 T[1, 1] := 1; T[n_, 1] := 1; T[n_, n_] := 1; T[n_, k_] := (1 - (-1)^(n - k + 1))/2; Table[T[n, k], {n, 1, 10}, {k, 1, n}]//Flatten (* _G. C. Greubel_, Dec 05 2016 *)
%t A135839 Flatten[Table[Join[{1},PadLeft[{},n,{0,1}]],{n,0,20}]] (* _Harvey P. Dale_, Feb 26 2024 *)
%K A135839 nonn,tabl,easy
%O A135839 1,1
%A A135839 _Gary W. Adamson_, Dec 01 2007
%E A135839 Definition corrected by _Zhuorui He_, Jul 21 2025