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 A347316 #13 Apr 07 2025 13:46:44
%S A347316 1,1,2,1,0,3,1,2,1,1,1,1,1,0,0,4,1,2,1,0,1,2,1,1,2,0,2,0,1,2,1,1,0,1,
%T A347316 1,2,1,1,1,0,1,1,1,1,1,2,1,1,0,1,2,1,1,1,1,1,1,2,1,0,1,2,1,0,2,2,0,1,
%U A347316 2,0,1,1,1,2,1,0,0,1,2,1,1,1,1,1,1,3,1,2,0,0,2,0,2,1,1,1,2,1,1,1
%N A347316 Irregular triangle read by rows: T(n,k) = number of times k appears in n-th row of A342585, n >= 0.
%H A347316 Michael De Vlieger, <a href="/A347316/b347316.txt">Table of n, a(n) for n = 0..10295</a> (rows 0 <= n <= 108, flattened)
%e A347316 Triangle begins:
%e A347316 1,
%e A347316 1,2,
%e A347316 1,0,3,
%e A347316 1,2,1,1,1,
%e A347316 1,1,0,0,4,
%e A347316 1,2,1,0,1,2,1,
%e A347316 ...
%e A347316 Row 4 of A342585 is [4, 4, 4, 1, 4, 0], containing one 0, one 1, and four 4's; so row 4 here is [1, 1, 0, 0, 4].
%t A347316 Block[{c, k, m, nn = 12}, c[0] = 1; Join[{{1}}, Map[Function[w, {1}~Join~Array[If[ListQ[#], Length[#], 0] &@ Lookup[w, #] &, Max@ Keys[w]]]@ KeySort@ PositionIndex[#] &, SplitBy[Reap[Do[k = 0; While[IntegerQ[c[k]], Set[m, c[k]]; Sow[m]; If[IntegerQ@ c[m], c[m]++, c[m] = 1]; k++]; Sow[0]; c[0]++, nn]][[-1, -1]], # == 0 &][[1 ;; -1 ;; 2]]]] ] // Flatten (* _Michael De Vlieger_, Oct 12 2021 *)
%Y A347316 Cf. A342585, A347299 (row sums).
%K A347316 nonn,tabf
%O A347316 0,3
%A A347316 _N. J. A. Sloane_, Sep 09 2021
%E A347316 More terms from _Alois P. Heinz_, Sep 09 2021