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 A135840 #11 Mar 27 2022 22:26:51
%S A135840 1,2,1,2,1,1,3,2,1,1,3,2,2,1,1,4,3,2,2,1,1,4,3,3,2,2,1,1,5,4,3,3,2,2,
%T A135840 1,1,5,4,4,3,3,2,2,1,1,6,5,4,4,3,3,2,2,1,1,6,5,5,4,4,3,3,2,2,1,1,7,6,
%U A135840 5,5,4,4,3,3,2,2,1,1,7,6,6,5,5,4,4,3,3,2,2,1,1,8,7,6,6,5,5,4,4,3,3,2,2,1,1
%N A135840 A135839 * A000012 as infinite lower triangular matrices.
%C A135840 Row sums = A004652 starting (1, 3, 4, 7, 9, 13, 16, 21, ...).
%H A135840 G. C. Greubel, <a href="/A135840/b135840.txt">Table of n, a(n) for the first 50 rows</a>
%F A135840 T(1, 1) = 1, T(n, 1) = floor((n + 2)/2), T(n, n) = 1, T(n, k) = floor((n - k + 2)/2). - _G. C. Greubel_, Dec 05 2016
%e A135840 First few rows of the triangle:
%e A135840 1;
%e A135840 2, 1;
%e A135840 2, 1, 1;
%e A135840 3, 2, 1, 1;
%e A135840 3, 2, 2, 1, 1;
%e A135840 4, 3, 2, 2, 1, 1;
%e A135840 4, 3, 3, 2, 2, 1, 1;
%e A135840 5, 4, 3, 3, 2, 2, 1, 1;
%e A135840 ...
%t A135840 T[1, 1] := 1; T[n_, 1] := Floor[(n + 2)/2]; T[n_, n_] := 1; T[n_, k_] := Floor[(n - k + 2)/2]; Table[T[n, k], {n, 1, 8}, {k, 1, n}]//Flatten (* _G. C. Greubel_, Dec 05 2016 *)
%Y A135840 Cf. A135839, A004652, A135841.
%K A135840 nonn
%O A135840 1,2
%A A135840 _Gary W. Adamson_, Dec 01 2007