A143972 Eigentriangle by rows, A143971 * (A108300 * 0^(n-k)); 1<=k<=1.

1, 4, 1, 7, 4, 5, 10, 7, 20, 16, 13, 10, 35, 64, 53, 16, 13, 50, 112, 212, 175, 19, 16, 65, 160, 371, 700, 578, 22, 19, 80, 208, 530, 1225, 2312, 1909, 25, 28, 95, 256, 689, 1750, 4046, 7636, 6305, 28, 25, 110, 304, 848, 2275, 5780, 23363, 25220, 20824

Offset: 1

Author

Gary W. Adamson, Sep 06 2008

Keywords

• nonn
• tabl

Comments

Right border = A108300: (1, 1, 5, 16, 53, 175, 578,...). Row sums = (1, 5, 16, 53, 175, 578,...) = INVERT transform of (1, 4, 7, 10,...).

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

Comment in A108300 states that (5, 16, 53, 175,...) is related to the numbers of hydrogen bonds in hydrocarbons.

Examples

			First few rows of the triangle =
1;
4, 1;
7, 4, 5;
10, 7, 10, 16;
13, 10, 35, 64, 53;
16, 13, 50, 112, 212, 175;
19, 16, 65, 160, 371, 700, 578;
22, 19, 80, 208, 530, 1225, 2312, 1909;
25, 22, 95, 256, 689, 1750, 4046, 7636, 6305;
... Example: row 4 = (10, 7, 20, 16) = termwise products of (10, 7, 4, 1) and (1, 1, 5, 16) = (10*1, 7*1, 4*5, 1*16), where (10, 7, 4, 1) = row 4 of triangle A143971.
		

Crossrefs

A143971, Cf. A016777, A108300

Formula

Eigentriangle by rows, A143971 * (A108300 * 0^(n-k)); 1<=k<=1

Triangle A143971 = (1; 4,1; 7,4,1; 10,7,4,1;...). A108300 * 0^(n-k) = an infinite lower triangular matrix with A108300 (1, 1, 5, 16, 53, 175, 578, 1909,...) in the main diagonal and the rest zeros. By rows, = termwise products of n-th row terms of A143971 and n terms of A108300.