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

1,2

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.

Links

Table of n, a(n) for n=1..55.

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.

Example

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

Sequence in context: A143971 A367898 A016688 * A019651 A262606 A286387

Adjacent sequences: A143969 A143970 A143971 * A143973 A143974 A143975

Keyword

nonn,tabl

Author

Gary W. Adamson, Sep 06 2008

Status

approved