

A177878


Triangle in which row n is generated from (1,2,3,...,n) dot (n, n1,...,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
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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(i1), 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



