A159974 Triangle read by rows, M * Q; M = an infinite lower triangular Toeplitz matrix with (1, 1, 2, 3, 4, 5, ...) in every column. Q = a matrix with A034943: (1, 1, 2, 5, 12, 28, ...) as the main diagonal and the rest zeros.

1, 1, 1, 2, 1, 2, 3, 2, 2, 5, 4, 3, 4, 5, 12, 5, 4, 6, 10, 12, 28, 6, 5, 8, 15, 24, 28, 65, 7, 6, 10, 20, 36, 56, 65, 151, 8, 7, 12, 25, 48, 84, 130, 151, 351, 9, 8, 14, 30, 60, 112, 195, 302, 351, 816, 10, 9, 16, 35, 72, 140, 260, 453, 702, 816, 1897

Offset: 2

Author

Gary W. Adamson, Apr 28 2009

Keywords

• nonn
• tabl

Comments

Row sums = A034943 starting (1, 2, 5, 12, 28, 65, 151, 351, ...).

As a property of eigentriangles, sum of n-th row terms = rightmost term of next row.

A034943 starting (1, 2, 5, 12, 28, ...) = the INVERT transform of (1, 1, 2, 3, 4, 5, ...).

Examples

			First few rows of the triangle:
   1;
   1, 1;
   2, 1,  2;
   3, 2,  2,  5;
   4, 3,  4,  5, 12;
   5, 4,  6, 10, 12,  28;
   6, 5,  8, 15, 24,  28,  65;
   7, 6, 10, 20, 36,  56,  65, 151;
   8, 7, 12, 25, 48,  84, 130, 151, 351;
   9, 8, 14, 30, 60, 112, 195, 302, 351, 816;
  10, 9, 16, 35, 72, 140, 260, 453, 702, 816, 1897;
  ...
Example: row 6 = (4, 3, 4, 5, 12) = termwise products of (1, 1, 2, 5, 12) and (4, 3, 2, 1, 1).
		

Crossrefs

Cf. A034943.

Formula

Triangle read by rows, M * Q; M = an infinite lower triangular Toeplitz matrix with (1, 1, 2, 3, 4, 5, ...) in every column. Q = a matrix with A034943: (1, 1, 2, 5, 12, 28, ...) as the main diagonal and the rest zeros.