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

Offset

0,3

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).

Links

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

Example

.   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  .

Prog

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

Crossrefs

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

Sequence in context: A153907 A029306 A337511 * A341216 A116491 A131325

Adjacent sequences: A261360 A261361 A261362 * A261364 A261365 A261366

Keyword

nonn,tabl

Author

Reinhard Zumkeller, Aug 16 2015

Status

approved