A077605 Left summing matrix, S.

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

Table of n, a(n) for n=1..105.

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

Adjacent sequences: A077602 A077603 A077604 * A077606 A077607 A077608

Keyword

easy,nonn,tabl

Author

Clark Kimberling, Nov 11 2002

Status

approved