OFFSET
0,2
COMMENTS
Carryovers (additive) are defined as "add current product to next product". For example: (1,2,3) dot (3,2,1) with carryovers = ((1*3=3), (2*2+3=7), (3*1+7=10)), so row 2 = (3, 7, 10).
FORMULA
By rows, (1,2,3,...) dot (...3,2,1); add current product to next product.
As an array, row 0 = the tetrahedral numbers, (1, 4, 10, 20, 35,...). n-th row adds n*(1, 3, 6, 10, 15,...) termwise.
EXAMPLE
Row 2 = (3, 7, 10) = (1, 2, 3) dot (3, 2, 1) with carryovers, thus: (3 = 1*3; 7 = 2*2 + 3; 10 = 3*1 + 7).
First few rows of the array:
1, 4, 10, 20, 35,...
2, 7, 16, 30, 50,...
3, 10, 22, 40, 65,...
...
Example: row 1 is obtained by adding (1, 3, 6, 10, 15,...) termwise to (1, 4, 10, 20, 35,...).
First few rows of the triangle:
1;
2, 4;
3, 7, 10;
4, 10, 16, 20;
5, 13, 22, 30, 35;
6, 16, 28, 40, 50, 56;
7, 19, 34, 50, 65, 77, 84;
8, 22, 40, 60, 80, 98, 112, 120;
9, 25, 46, 70, 95, 119, 140, 156, 165;
10, 28, 52, 80, 110, 140, 168, 192, 210, 220;
...
CROSSREFS
KEYWORD
AUTHOR
Gary W. Adamson, Dec 13 2010
STATUS
approved
