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%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
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