[seqfan] 2X2 -n..n with inverse in -n..n and totient function?

[Ron Hardin]

Toying around with 2X2 -n..n matrices whose determinant divides every entry, is 
this obvious?  Not to me.

1/8 the number of 2X2 -n..n arrays with a 2X2 -n..n inverse, i.e. with 
determinant dividing every element

 5 13 29 45 77 93 141 173 221 253 333 365 461 509 573 637 765 813 957 1021 1117 
1197 1373 1437 1597 1693 1837

first differences

 8 16 16 32 16 48 32 48 32 80 32 96 48 64 64 128 48 144 64 96 80 176 64 160 96 
144 96 224 64 240 128 160 128 192

first differences / 8

1 2 2 4 2 6 4 6 4 10 4 12 6 8 8 16 6 18 8 12 10 22 8 20 12 18 12 28 8 30 16 20 
16 24 12 36 18 24 16 40 12 42 20

= A000010(n+1)

Another mystery is why the original series was divisible by 8 in the first 
place.


 rhhardin at mindspring.com
rhhardin at att.net (either)