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A077605
Left summing matrix, S.
1
1, 1, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0
OFFSET
1,1
COMMENTS
If v is a sequence written as a column vector, then Sv is the sequence of partial sums of v. The inverse of S is the left differencing matrix; the transpose of S is the right summing matrix.
LINKS
Clark Kimberling, Matrix Transformations of Integer Sequences, J. Integer Seqs., Vol. 6, 2003.
FORMULA
S(n, k)=1 if 1<=k<=n, else S(n, k)=0.
EXAMPLE
Northwest corner:
1 0 0 0 0
1 1 0 0 0
1 1 1 0 0
1 1 1 1 0
1 1 1 1 1
CROSSREFS
Cf. A077606 (matrix inverse), A101688 (transpose).
Sequence in context: A286755 A286349 A145575 * A323512 A014672 A015335
KEYWORD
easy,nonn,tabl
AUTHOR
Clark Kimberling, Nov 11 2002
STATUS
approved