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

0,2

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,...).

Links

Table of n, a(n) for n=0..44.

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.

Example

 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

Sequence in context: A085753 A120008 A162197 * A212225 A278085 A356195

Adjacent sequences: A160767 A160768 A160769 * A160771 A160772 A160773

Keyword

nonn,tabl

Author

Gary W. Adamson, Dec 15 2010

Status

approved