OFFSET
1,4
COMMENTS
Rows are of lengths 2, 5, 10, ..., i^2+1,....
Every row starts with k = 0. For all n: T(n, 0) = 1.
The numbers are found by an exhaustive search among all (n^2, k)-combinations of 1's.
Another description of the sequence: Given a square grid with side n and n^2 points, T(n,k) is the number of ways to choose k points of the grid, so that no 4 of the chosen points form a square with sides parallel to the grid.
LINKS
Heinrich Ludwig, Table of n, a(n) for n = 1..147
Heinrich Ludwig, CSV file for spreadsheets
EXAMPLE
T(n, k) written as a triangle
1,1;
1,4,6,4,0;
1,9,36,84,121,101,38,4,0,0;
1,16,120,560,1806,4200,7096,8532,6929,3444,876,84,2,0,0,0,0;
...
For n = 4 there are 2 matrices with exactly k = 12 1's so that no more than three 1's are in the corners of any square sub-block.
[0 1 1 1] [1 1 1 0]
[1 1 0 1] [1 0 1 1]
[1 0 1 1] [1 1 0 1]
[1 1 1 0] [0 1 1 1]
CROSSREFS
KEYWORD
tabf,nonn,hard
AUTHOR
Heinrich Ludwig, Jul 12 2013
STATUS
approved