A358549 Triangle read by rows where row n is reversed partial sums of row n of the Sierpinski triangle (A047999).

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, 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, 6, 5, 4, 4, 4, 4, 4, 3, 2, 1, 4, 3, 3, 3, 3, 2, 2, 2, 2, 1, 1, 1, 1

Offset: 0

Author

Gary W. Adamson, Nov 21 2022

Keywords

• nonn
• tabl
• easy

Comments

Row reversal of A261363 (which is the main entry).

These sums can be formed by taking A047999 as a lower triangular matrix times an all-1's lower triangular matrix.

Examples

			Triangle begins:
      k=0  1  2  3  4  5  6  7  8
  n=0:  1;
  n=1:  2, 1;
  n=2:  2, 1, 1;
  n=3:  4, 3, 2, 1;
  n=4:  2, 1, 1, 1, 1;
  n=5:  4, 3, 2, 2, 2, 1;
  n=6:  4, 3, 3, 2, 2, 1, 1;
  n=7:  8, 7, 6, 5, 4, 3, 2, 1;
  n=8:  2, 1, 1, 1, 1, 1, 1, 1, 1;
For n=5, row 5 here and row 5 of A047999 are:
  row      4, 3, 2, 2, 2, 1
  sums of  1, 1, 0, 0, 1, 1
		

Crossrefs

Cf. A047999, A261363 (rows reversed).

Cf. A001316 (column k=0), A000012 (main diagonal).

Programs

Mathematica

row[n_] := Reverse[Accumulate[Array[Boole[0 == BitAnd[n-#, #]] &, n + 1, 0]]]; Array[row, 13, 0] // Flatten (* Amiram Eldar, May 13 2025 *)

Formula

T(n,k) = Sum_{i=k..n} A047999(n,i).