A358549 - OEIS

%I #28 Dec 03 2022 23:46:23

%S 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,

%T 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,

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

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

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

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

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

%e Triangle begins:

%e       k=0  1  2  3  4  5  6  7  8

%e   n=0:  1;

%e   n=1:  2, 1;

%e   n=2:  2, 1, 1;

%e   n=3:  4, 3, 2, 1;

%e   n=4:  2, 1, 1, 1, 1;

%e   n=5:  4, 3, 2, 2, 2, 1;

%e   n=6:  4, 3, 3, 2, 2, 1, 1;

%e   n=7:  8, 7, 6, 5, 4, 3, 2, 1;

%e   n=8:  2, 1, 1, 1, 1, 1, 1, 1, 1;

%e For n=5, row 5 here and row 5 of A047999 are:

%e   row      4, 3, 2, 2, 2, 1

%e   sums of  1, 1, 0, 0, 1, 1

%Y Cf. A047999, A261363 (rows reversed).

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

%K nonn,tabl,easy

%O 0,2

%A _Gary W. Adamson_, Nov 21 2022