A261363 Triangle read by rows: partial row sums of Sierpinski's triangle.

1, 1, 2, 1, 1, 2, 1, 2, 3, 4, 1, 1, 1, 1, 2, 1, 2, 2, 2, 3, 4, 1, 1, 2, 2, 3, 3, 4, 1, 2, 3, 4, 5, 6, 7, 8, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 2, 2, 2, 2, 2, 2, 3, 4, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 4, 1, 2, 3, 4, 4, 4, 4, 4, 5, 6, 7, 8, 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 4

Offset: 0

Author

Reinhard Zumkeller, Aug 16 2015

Keywords

• nonn
• tabl
• easy

Comments

T(n,n) = number of distinct terms in row n = number of odd terms in row n+1 = A001316(n).

Central terms, for n > 0: T(2*n,n) = A048896(n-1).

Examples

			.   n |  Sierpinski: A047999(n,*)  |  Partial row sums: T(n,*)
. ----+----------------------------+----------------------------
.   0 |              1             |              1
.   1 |             1 1            |             1 2
.   2 |            1 0 1           |            1 1 2
.   3 |           1 1 1 1          |           1 2 3 4
.   4 |          1 0 0 0 1         |          1 1 1 1 2
.   5 |         1 1 0 0 1 1        |         1 2 2 2 3 4
.   6 |        1 0 1 0 1 0 1       |        1 1 2 2 3 3 4
.   7 |       1 1 1 1 1 1 1 1      |       1 2 3 4 5 6 7 8
.   8 |      1 0 0 0 0 0 0 0 1     |      1 1 1 1 1 1 1 1 2
.   9 |     1 1 0 0 0 0 0 0 1 1    |     1 2 2 2 2 2 2 2 3 4
.  10 |    1 0 1 0 0 0 0 0 1 0 1   |    1 1 2 2 2 2 2 2 3 3 4
.  11 |   1 1 1 1 0 0 0 0 1 1 1 1  |   1 2 3 4 4 4 4 4 5 6 7 8
.  12 |  1 0 0 0 1 0 0 0 1 0 0 0 1 |  1 1 1 1 2 2 2 2 3 3 3 3 4  .
		

Links

• Reinhard Zumkeller, Rows n = 0..125 of triangle, flattened

Crossrefs

Cf. A047999, A008949, A048896 (central terms), A001316 (right edge), A261366.

Programs

Haskell

a261363 n k = a261363_tabl !! n !! k
a261363_row n = a261363_tabl !! n
a261363_tabl = map (scanl1 (+)) a047999_tabl

Mathematica

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