A104582 Triangle read by rows: T(i,j) is the (i,j)-entry (1 <= j <= i) of the product of the lower triangular matrix (Fibonacci(i-j+1)) and of the lower triangular matrix all of whose entries are equal to 1 (for j <= i).

1, 2, 1, 4, 2, 1, 7, 4, 2, 1, 12, 7, 4, 2, 1, 20, 12, 7, 4, 2, 1, 33, 20, 12, 7, 4, 2, 1, 54, 33, 20, 12, 7, 4, 2, 1, 88, 54, 33, 20, 12, 7, 4, 2, 1, 143, 88, 54, 33, 20, 12, 7, 4, 2, 1, 232, 143, 88, 54, 33, 20, 12, 7, 4, 2, 1, 376, 232, 143, 88, 54, 33, 20, 12, 7, 4, 2, 1, 609, 376, 232

Offset: 1

Author

Gary W. Adamson, Mar 16 2005

Keywords

• nonn
• tabl

Examples

			The first few rows of the triangle are:
   1;
   2, 1;
   4, 2, 1;
   7, 4, 2, 1;
  12, 7, 4, 2, 1;
  ...
		

Crossrefs

Sum of row n = Fibonacci(n+4) - n - 3 (A001924). Columns (starting from the diagonal entries) are the Fibonacci numbers -1 (A000071).

Programs

Maple

with(combinat): for i from 1 to 13 do seq(fibonacci(i-j+3)-1,j=1..i) od; # yields sequence in triangular form # Emeric Deutsch, Mar 23 2005

Formula

T(i, j) = Fibonacci(i-j+3) - 1 for 1 <= j <= i and 0 otherwise. - Emeric Deutsch, Mar 23 2005

Extensions

More terms from Emeric Deutsch, Mar 23 2005