A177877 Triangle in which row n is derived from (1,2,3,...,n) dot (n,n-1,...,1) with additive carryovers.

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

Offset: 0

Author

Gary W. Adamson, Dec 13 2010

Keywords

• nonn
• tabl
• easy

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).

Examples

			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

Cf. A002415 (row sums).

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.