A144963 Eigentriangle, row sums = A000081 starting (1, 2, 4, 9, 20, 48, 115, ...).

1, 1, 1, 1, 1, 2, 2, 1, 2, 4, 3, 2, 2, 4, 9, 8, 3, 4, 4, 9, 20, 16, 8, 6, 8, 9, 20, 48, 41, 16, 16, 12, 18, 20, 48, 115, 98, 41, 32, 32, 27, 40, 115, 286, 250, 98, 82, 64, 72, 60, 96, 115, 286, 719

Offset

1,6

Comments

Row sums = A000081 starting with offset 2: (1, 2, 4, 9, 20, 48, 115, ...).

Right border = (1, 1, 2, 4, 9, 20, 48, ...).

Left border = A051573: (1, 1, 1, 2, 3, 8, 16, 41, ...).

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

Links

Table of n, a(n) for n=1..54.

Formula

Eigentriangle by rows, termwise products of A000081 starting with offset 2: (1, 2, 4, 9, 20, 48, ...) and row terms of an A051573 decrescendo triangle: (1; 1,1; 1,1,1; 2,1,1,1; 3,2,1,1,1; ...) where A051573 = (1, 1, 1, 2, 3, 8, 16, 41, ...).

Example

First few rows of the triangle:
   1;
   1,  1;
   1,  1,  2;
   2,  1,  2,  4;
   3,  2,  2,  4,  9;
   8,  3,  4,  4,  9, 20;
  16,  8,  6,  8,  9, 20, 48;
  41, 16, 16, 12, 18, 20, 48, 115;
  98, 41, 32, 32, 27, 40, 48, 115, 286;
  ...
Row 4 = (2, 1, 2, 4) = termwise products of (2, 1, 1, 1) and (1, 1, 2, 4).

Crossrefs

Sequence in context: A128176 A368415 A370075 * A305632 A329069 A035374

Adjacent sequences: A144960 A144961 A144962 * A144964 A144965 A144966

Keyword

eigen,nonn,tabl

Author

Gary W. Adamson, Sep 27 2008

Status

approved