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A177878 Triangle in which row n is generated from (1,2,3,...,n) dot (n, n-1,...,1) with subtractive carryovers. 2
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 (list; table; graph; refs; listen; history; text; internal format)
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

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Last modified February 17 17:27 EST 2018. Contains 299296 sequences. (Running on oeis4.)