A160770 Triangle in which row n is generated from (1,3,6,10,...n) dot (n,n-1,...1) with subtractive carryovers.

1, 3, 0, 6, 3, 3, 10, 8, 10, 0, 15, 15, 21, 9, 6, 21, 24, 36, 24, 21, 0, 28, 35, 55, 45, 45, 18, 10, 36, 48, 78, 72, 78, 48, 36, 0, 45, 63, 105, 105, 120, 90, 78, 30, 15

Offset: 0

Author

Gary W. Adamson, Dec 15 2010

Keywords

• nonn
• tabl

Comments

Row sums = A005995: (1, 3, 12, 28, 66, 126, 236,...); also generated from:

(1/2)*((1, 6, 21, 56, 126,...)+(1, 0, 3, 0, 6, 0, 10,...)); where (1, 6, 21,...) = bin(n,5).

A177878 = the analogous sequence using vector (1,2,3,...).

Examples

			First few rows of the triangle:
  1;
  3, 0;
  6, 3, 3;
  10, 8, 10, 0;
  15, 15, 21, 9, 6;
  21, 24, 36, 24, 21, 0;
  28, 35, 55, 45, 45, 18, 10;
  36, 48, 78, 72, 78, 48, 36, 0
  45, 63, 105, 105, 120, 90, 78, 30, 15;
  ...
Example: row 2 = (6, 3, 3) = (1, 3, 6) dot (6, 3, 1) with subtractive carryovers = ((1*6=6), (3*3-6=3), (6*1-3=3)) = (6, 3, 3).
		

Crossrefs

A005995, A177878

Formula

The subtractive carryover dot product of two vectors (a(1),a(2),...a(n)) dot (b(1),b(2),..b(n)) = (c(1),..,c(n)) is defined by c(1)=a(1)*b(1) and c(i) = a(i)*b(i)-c(i-1), i>1; where the vector = the triangular series.