A179806 Irregular triangle by rows, M*Q. M = triangle with (1,2,3,...) in every column, with the leftmost column shifted upwards one row. Q = a diagonalized variant of odd-indexed Fibonacci numbers.

1, 2, 3, 2, 4, 4, 5, 5, 6, 10, 13, 6, 8, 15, 26, 34, 7, 10, 20, 39, 68, 89, 8, 12, 25, 52, 102, 178, 233, 9, 14, 30, 65, 136, 267, 466, 610, 10, 16, 35, 78, 170, 356, 699, 1220, 1597

Offset: 1

Author

Gary W. Adamson, Jul 28 2010

Keywords

• nonn
• tabf

Comments

Row sums = the odd-indexed Fibonacci numbers, A001519, starting with offset 1.

Sums of row terms = (1, 2, 5, 13, 34, 89, ...).

For rows > 1, sum of n-th row terms = rightmost term of next row.

Examples

			First few rows of the triangle:
   1;
   2;
   3,  2;
   4,  4,  5;
   5,  6, 10,  13;
   6,  8, 15,  26,  34;
   7, 10, 20,  39,  68,  89;
   8, 12, 25,  52, 102, 178,  233;
   9, 14, 30,  65, 136, 267,  466,  610;
  10, 16, 35,  78, 170, 356,  699, 1220, 1597;
  11, 18, 40,  91, 204, 445,  932, 1830, 3194, 4181;
  12, 20, 45, 104, 238, 534, 1165, 2440, 4791, 8362, 10946;
  ...
		

Crossrefs

Cf. A001519.

Formula

Triangle, M*Q; where M = a triangle with (1,2,3,...) in every column with the leftmost column shifted upwards one row. Q = an infinite matrix with the odd-indexed Fibonacci numbers as the right border: (1, 2, 5, 13,...) and

the rest zeros.