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## Homework Statement

I don't know if this has ties to linear algebra, so sorry in advance if i'm posting in a wrong section.

We have an n*n matrix A, n is an odd number, and "the matrix's sides are 0" meaning:

we'll call non-zero elements as 1's for now.

1st line 1111...1111

2nd line 0111...1110

3rd line 0011...1100

...

...

n-2 00111..11100

(n-1) 01111...1110

n 1111.....1111

the diagonals are intact.

For example for n=3, this would be the matrix

111

010

111

for n=5

11111

01110

00100

01110

11111

etc

Now, the problem states that all non-zero data are stored in a 1-D array row by row, B[N-1], where N-1 the total number of nonzero elements(array index starts at 0).

We are asked to a)find a formula to correlate a non-zero element's coordinates in A with its position (array index) in array B.

For example for n=3, for the matrix A:

abc

0d0

efg

B would be b=[a,b,c,d,e,f,g], each non-zero elemet's position in B 0,1...6 respectively, and each nonzero element's coordinates {0,0}{0,1}{0,2}{1,1}{2,0}{2,1}{2,2} respectively.

and b) find a formula for the number of non-zero elements in A.

## Homework Equations

?

## The Attempt at a Solution

I found b), as

[Sum {from 1 to (n div 2)} 4*n ] + n , where div is integer division

as for a), i am trying to find a relation between i,j values, and their position in B, by trial and error, with only error so far.Any ideas?