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

1,2

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.

Links

Table of n, a(n) for n=1..45.

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.

Example

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

Sequence in context: A377703 A239626 A076363 * A071168 A091926 A325685

Adjacent sequences: A143862 A143863 A143864 * A143866 A143867 A143868

Keyword

nonn,tabl

Author

Gary W. Adamson, Sep 04 2008

Status

approved