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 A358549 #32 May 13 2025 02:40:03
%S A358549 1,2,1,2,1,1,4,3,2,1,2,1,1,1,1,4,3,2,2,2,1,4,3,3,2,2,1,1,8,7,6,5,4,3,
%T A358549 2,1,2,1,1,1,1,1,1,1,1,4,3,2,2,2,2,2,2,2,1,4,3,3,2,2,2,2,2,2,1,1,8,7,
%U A358549 6,5,4,4,4,4,4,3,2,1,4,3,3,3,3,2,2,2,2,1,1,1,1
%N A358549 Triangle read by rows where row n is reversed partial sums of row n of the Sierpinski triangle (A047999).
%C A358549 Row reversal of A261363 (which is the main entry).
%C A358549 These sums can be formed by taking A047999 as a lower triangular matrix times an all-1's lower triangular matrix.
%F A358549 T(n,k) = Sum_{i=k..n} A047999(n,i).
%e A358549 Triangle begins:
%e A358549 k=0 1 2 3 4 5 6 7 8
%e A358549 n=0: 1;
%e A358549 n=1: 2, 1;
%e A358549 n=2: 2, 1, 1;
%e A358549 n=3: 4, 3, 2, 1;
%e A358549 n=4: 2, 1, 1, 1, 1;
%e A358549 n=5: 4, 3, 2, 2, 2, 1;
%e A358549 n=6: 4, 3, 3, 2, 2, 1, 1;
%e A358549 n=7: 8, 7, 6, 5, 4, 3, 2, 1;
%e A358549 n=8: 2, 1, 1, 1, 1, 1, 1, 1, 1;
%e A358549 For n=5, row 5 here and row 5 of A047999 are:
%e A358549 row 4, 3, 2, 2, 2, 1
%e A358549 sums of 1, 1, 0, 0, 1, 1
%t A358549 row[n_] := Reverse[Accumulate[Array[Boole[0 == BitAnd[n-#, #]] &, n + 1, 0]]]; Array[row, 13, 0] // Flatten (* _Amiram Eldar_, May 13 2025 *)
%Y A358549 Cf. A047999, A261363 (rows reversed).
%Y A358549 Cf. A001316 (column k=0), A000012 (main diagonal).
%K A358549 nonn,tabl,easy
%O A358549 0,2
%A A358549 _Gary W. Adamson_, Nov 21 2022