A180264 Triangle, row sums = A006054; derived from an infinite lower triangular matrix with (1,1,1,...) as the leftmost column and (1,2,1,1,1,...) as other columns.

1, 1, 1, 2, 2, 1, 1, 1, 4, 5, 1, 1, 2, 10, 11, 1, 1, 2, 5, 22, 25, 1, 1, 2, 5, 11, 50, 56, 1, 1, 2, 5, 11, 50, 56, 1, 1, 2, 5, 11, 25, 112, 126, 1, 1, 2, 5, 11, 25, 56, 252, 283, 1, 1, 2, 5, 11, 25, 56, 126, 566, 636, 1, 1, 2, 5, 11, 25, 56, 126, 283, 1272, 1429

Offset: 1

Author

Gary W. Adamson, Aug 21 2010

Keywords

• nonn
• tabf

Comments

Row sums = A006054 starting (1, 2, 5, 11, 25, 56, 126,...).

Sum of n-th row terms = rightmost term of next row.

Examples

			First few rows of the triangle =
.
1;
1, 1;
1, 2, 2;
1, 1, 4, 5;
1, 1, 2, 10, 11;
1, 1, 2, 5, 22, 25;
1, 1, 2, 5, 11, 50, 56;
1, 1, 2, 5, 11, 25, 112, 126;
1, 1, 2, 5, 11, 25, 56, 252, 283;
1, 1, 2, 5, 11, 25, 56, 126, 566, 636;
1, 1, 2, 5, 11, 25, 56, 126, 283, 1272, 1429;
1, 1, 2, 5, 11, 25, 56, 126, 283, 636, 2858, 3211;
...
Example: Row 4 = (1, 1, 4, 5) = termwise products of (1, 1, 2, 1) and (1, 1, 2, 5).
		

Crossrefs

Cf. A006054

Formula

Let M = an infinite lower triangular matrix with 1's in the leftmost column,

and (1,2,1,1,1,...) as other columns. Let Q = a diagonalized variant of

A006054 (1, 1, 2, 5, 11, 25, 56,...) as the right border and the rest zeros.

Triangle A180264 = M*Q.