A180262 Triangle by rows, generated from a triangle with (1,2,1,1,1,...) in every column.

1, 2, 1, 1, 2, 3, 1, 1, 6, 6, 1, 1, 3, 12, 14, 1, 1, 3, 6, 28, 31, 1, 1, 3, 6, 14, 62, 70, 1, 1, 3, 6, 14, 31, 140, 157, 1, 1, 3, 6, 14, 31, 70, 314, 353, 1, 1, 3, 6, 14, 31, 70, 157, 706, 793, 1, 1, 3, 6, 14, 31, 70, 157, 353, 1586, 1782

Offset

0,2

Comments

Row sums = A006356: (1, 3, 6, 14, 31, 70, 157, 353,...).

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

Links

Table of n, a(n) for n=0..65.

Formula

Let M be an infinite Toeplitz lower triangular matrix with (1,2,1,1,1,..) in every column. A180262 = M * a diagonalized variant of A006356 such that the main diagonal = A006356 prefaced with a 1: (1, 1, 3, 6, 14, 31,...) and the rest zeros.

Example

First few rows of the triangle:
  1;
  2, 1;
  1, 2, 3;
  1, 1, 6,  6;
  1, 1, 3, 12, 14;
  1, 1, 3,  6, 28, 31;
  1, 1, 3,  6, 14, 62,  70;
  1, 1, 3,  6, 14, 31, 140, 157;
  1, 1, 3,  6, 14, 31,  70, 314, 353;
  1, 1, 3,  6, 14, 31,  70, 157, 706,  793;
  1, 1, 3,  6, 14, 31,  70, 157, 353, 1586, 1782;
  1, 1, 3,  6, 14, 31,  70, 157, 353,  793, 3564, 4004;
  1, 1, 3,  6, 14, 31,  70, 157, 353,  793, 1782, 8008,  8997;
  1, 1, 3,  6, 14, 31,  70, 157, 353,  793, 1782, 4004, 17994, 20216;
  ...
Example: row 3 of the triangle = (1, 1, 6, 6) = termwise products of (1, 1, 2, 1) and (1, 1, 3, 6).

Crossrefs

Cf. A006356.

Sequence in context: A260876 A152650 A184219 * A161789 A109671 A141289

Adjacent sequences: A180259 A180260 A180261 * A180263 A180264 A180265

Keyword

nonn,tabl

Author

Gary W. Adamson, Aug 21 2010

Status

approved