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Triangle read by rows: partial row sums of Sierpinski's triangle.
7

%I #6 Aug 16 2015 17:28:23

%S 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,

%T 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,

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

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

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

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

%H Reinhard Zumkeller, <a href="/A261363/b261363.txt">Rows n = 0..125 of triangle, flattened</a>

%e . n | Sierpinski: A047999(n,*) | Partial row sums: T(n,*)

%e . ----+----------------------------+----------------------------

%e . 0 | 1 | 1

%e . 1 | 1 1 | 1 2

%e . 2 | 1 0 1 | 1 1 2

%e . 3 | 1 1 1 1 | 1 2 3 4

%e . 4 | 1 0 0 0 1 | 1 1 1 1 2

%e . 5 | 1 1 0 0 1 1 | 1 2 2 2 3 4

%e . 6 | 1 0 1 0 1 0 1 | 1 1 2 2 3 3 4

%e . 7 | 1 1 1 1 1 1 1 1 | 1 2 3 4 5 6 7 8

%e . 8 | 1 0 0 0 0 0 0 0 1 | 1 1 1 1 1 1 1 1 2

%e . 9 | 1 1 0 0 0 0 0 0 1 1 | 1 2 2 2 2 2 2 2 3 4

%e . 10 | 1 0 1 0 0 0 0 0 1 0 1 | 1 1 2 2 2 2 2 2 3 3 4

%e . 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

%e . 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 .

%o (Haskell)

%o a261363 n k = a261363_tabl !! n !! k

%o a261363_row n = a261363_tabl !! n

%o a261363_tabl = map (scanl1 (+)) a047999_tabl

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

%K nonn,tabl

%O 0,3

%A _Reinhard Zumkeller_, Aug 16 2015