

A160770


Triangle in which row n is generated from (1,3,6,10,...n)dot(n,n1,...1) with subtractive carryovers.


2



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
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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(i1), 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*36=3), (6*13=3) = (6, 3, 3).


CROSSREFS

A005995, A177878
Sequence in context: A085753 A120008 A162197 * A212225 A051021 A215664
Adjacent sequences: A160767 A160768 A160769 * A160771 A160772 A160773


KEYWORD

nonn,tabl


AUTHOR

Gary W. Adamson, Dec 15 2010


STATUS

approved



