A143865 Eigentriangle of A099375 (odd number subsequences decrescendo).

1, 3, 1, 5, 3, 4, 7, 5, 12, 12, 9, 7, 20, 36, 36, 11, 9, 28, 60, 108, 108, 13, 11, 36, 84, 180, 324, 324, 15, 13, 44, 108, 252, 540, 972, 972, 17, 15, 52, 132, 324, 756, 1620, 2916, 2916

Offset: 1

Author

Gary W. Adamson, Sep 04 2008

Keywords

• nonn
• tabl

Comments

The product A099375 * (A003946 * 0^(n-k)) creates a new eigentriangle with rows = termwise product of odd descrendo terms, e.g.: (7, 5, 3, 1) and first n terms of (1, 1, 4, 12,). The resulting triangle has row sums = (1, 4, 12, 36, 108,...), right border = (1, 1, 4, 12, 36,...) and the property that sum of n-th row terms = rightmost term of next row.

Examples

			First few rows of the triangle = 1; 3, 1; 5, 3, 4; 7, 5, 12, 12; 9, 7, 20, 36, 36; 11, 9, 28, 60, 108, 108; 13, 11, 36, 84, 180, 324, 324; ... Row 4 = termwise product of (7, 5, 3, 1) and (1, 1, 4, 12) = (7*1, 5*1, 3*4, 1*12).
		

Crossrefs

A099375, Cf. A003946

Formula

Triangle read by rows, A099375: (1; 3,1; 5,3,1;...) * (A003946 * 0^(n-k)); 1<=k<=n. (A003946 * 0^(n-k) = an infinite lower triangular matrix with shifted A003946: (1, 1, 4, 12, 36, 108,...) in the main diagonal and the rest zeros.