A177878 Triangle in which row n is generated from (1,2,3,...,n) dot (n, n-1,...,1) with subtractive carryovers.

1, 2, 0, 3, 1, 2, 4, 2, 4, 0, 5, 3, 6, 2, 3, 6, 4, 8, 4, 6, 0, 7, 5, 10, 6, 9, 3, 4, 8, 6, 12, 8, 12, 6, 8, 0, 9, 7, 14, 10, 15, 9, 12, 4, 5, 10, 8, 16, 12, 18, 12, 16, 8, 10, 0, 11, 9, 18, 14, 21, 15, 20, 12, 15, 5, 6, 12, 10, 20, 16, 24, 18, 24, 16, 20, 10, 12, 0

Offset

0,2

Comments

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.

Row sums = A005993: (1, 2, 6, 10, 19, 28,...)

A177877 = analogous triangle with additive carryovers.

A160770 = the analogous triangle using the triangular series as the generating vector.

Links

Table of n, a(n) for n=0..77.

Formula

By rows, dot product of (1,2,3,...) and (...3,2,1) with subtractive carryovers; such that current row product subtracts previous product.

Example

Row 3 = (4, 2, 4, 0) = (1, 2, 3, 4) dot (4, 3, 2, 1) with subtractive carryovers = (4), then (2*3 - 4 = 2), (3*2 - 2 = 4), and (4*1 - 4 = 0).
First few rows of the triangle =
.
1;
2, 0;
3, 1, 2;
4, 2, 4, 0;
5, 3, 6, 2, 3;
6, 4, 8, 4, 6, 0;
7, 5, 10, 6, 9, 3, 4;
8, 6, 12, 8, 12, 6, 8, 0;
9, 7, 14, 10, 15, 9, 12, 4, 5;
10, 8, 16, 12, 18, 12, 16, 8, 10, 0;
11, 9, 18, 14, 21, 15, 20, 12, 15, 5, 6;
12, 10, 20, 16, 24, 18, 24, 16, 20, 10, 12, 0;
...

Crossrefs

Cf. A005993, A177877, A160770

Sequence in context: A259598 A096067 A098861 * A125940 A071504 A125943

Adjacent sequences: A177875 A177876 A177877 * A177879 A177880 A177881

Keyword

nonn,tabl

Author

Gary W. Adamson, Dec 13 2010

Status

approved