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A160770 Triangle in which row n is generated from (1,3,6,10,...n)dot(n,n-1,...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 (list; table; graph; refs; listen; history; text; internal format)
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 A051021

Adjacent sequences:  A160767 A160768 A160769 * A160771 A160772 A160773

KEYWORD

nonn,tabl

AUTHOR

Gary W. Adamson, Dec 15 2010

STATUS

approved

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Last modified December 8 04:27 EST 2016. Contains 278902 sequences.