OFFSET
1,1
COMMENTS
The positions reflect radii which are a unique sum of two distinct square integers where order doesn't matter.
The positions are more frequent in occurrence than the positions where the first differences equal -2 because when the radius changes from exactly an integer value k to the open interval (k,k+1), the number of edge squares increases by 2, while in the reverse case, an increase from the open interval (k,k+1) to exactly k+1, the number of edge squares stays the same. This is in contrast to positions where the first difference equals 1 which are exactly balanced by positions which equal -1 .
LINKS
Rajan Murthy, Table of n, a(n) for n = 1..1553
EXAMPLE
a(2) = 7 corresponding to the shift from squared radius of 4 to (4,5). This also marks a shift of the radius from 2 to (2,3). The preceding shift, A235141(6), from radius in the interval (1,2) to 2 and squared radius in the interval (2,4) to 4 does not change the number of edge squares.
a(3) = 9 corresponding to the shift from squared radius of 5 to (5,8). The radius however remains in the interval (2,3). The preceding shift, A235141(8), from squared radius in the interval (4,5) to 5 results in a decrease of two due to the completion of the squares with upper right hand corner coordinates of x=1, y =2 and x=2, y=1 (since 5 = 1^2+2^2).
CROSSREFS
KEYWORD
nonn
AUTHOR
Rajan Murthy, Jan 08 2014
STATUS
approved