OFFSET
1,2
COMMENTS
The main entry for this topic is A239066.
A multigrade x1<=x2<=…<=xs; y1<=y2<=…<=ys is "symmetric" if x1+ys = x2+y(s-1) = … = xs+y1 when s is odd, or x1+xs = x2+x(s-1) = … = x(s/2)+x((s/2)+1) = y1+ys = y2+y(s-1) = … = y(s/2)+y((s/2)+1) when s is even. See A239067.
Any ideal multigrade x1,x2;y1,y2 of degree 1 is symmetric, since x1+x2 = y1+y2. Ideal non-symmetric multigrades are known only for degrees 2,3,4,5,6,7. The ones for degrees 5,6,7 are only conjecturally the smallest ones.
FORMULA
a(n^2 + n - 1) = 1 or 0.
EXAMPLE
1, 6, 9; 3, 3, 10
1, 10, 12, 23; 3, 5, 16, 22
1, 7, 17, 26, 30; 2, 5, 21, 22, 31
1, 10, 18, 35, 37, 47; 2, 7, 25, 26, 43, 45
1, 19, 20, 51, 57, 80, 82; 2, 12, 31, 40, 69, 71, 85
1, 8, 24, 51, 54, 82, 83, 97; 2, 6, 27, 43, 64, 73, 89, 96
1, 6, 9; 3, 3, 10 is an ideal non-symmetric multigrade of degree 2 as 1+10 != 6+3 and 1^1 + 6^1 + 9^1 = 16 = 3^1 + 3^1 + 10^1 and 1^2 + 6^2 + 9^2 = 118 = 3^2 + 3^2 + 10^2.
CROSSREFS
KEYWORD
hard,more,nonn,tabf
AUTHOR
Jonathan Sondow, Mar 10 2014
STATUS
approved