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. For non-symmetric ones, see A239068.
The ideal symmetric multigrades of degrees 5,6,7,8,9,10 are only conjecturally the smallest ones.
LINKS
C. Starr, Notes on Listener Crossword 4595 by Elap, The Mathematical Gazette (July 2021), Vol. 105, Issue 563, 291-298.
FORMULA
a(n^2 + n - 1) = 1 or 0.
EXAMPLE
1, 3; 2, 2
1, 4, 4; 2, 2, 5
1, 4, 5, 8; 2, 2, 7, 7
1, 5, 9, 17, 18; 2, 3, 11, 15, 19
1, 4, 6, 12, 14, 17; 2, 2, 9, 9, 16, 16
1, 19, 28, 59, 65, 90, 102; 2, 14, 39, 45, 76, 85, 103
1, 5, 10, 24, 28, 42, 47, 51; 2, 3, 12, 21, 31, 40, 49, 50
1, 25, 31, 84, 87, 134, 158, 182, 198; 2, 18, 42, 66, 113, 116, 169, 175, 199
1, 13, 126, 214, 215, 413, 414, 502, 615, 627; 6, 7, 134, 183, 243, 385, 445, 494, 621, 622
1, 4, 4; 2, 2, 5 is an ideal symmetric multigrade of degree 2 as 1+5 = 4+2 = 4+2 and 1^1 + 4^1 + 4^1 = 9 = 2^1 + 2^1 + 5^1 and 1^2 + 4^2 + 4^2 = 33 = 2^2 + 2^2 + 5^2.
1, 4, 5, 8; 2, 2, 7, 7 is an ideal symmetric multigrade of degree 3 as 1+8 = 4+5 = 2+7 = 2+7 and 1^1 + 4^1 + 5^1 + 8^1 = 18 = 2^1 + 2^1 + 7^1 + 7^1 and 1^2 + 4^2 + 5^2 + 8^2 = 106 = 2^2 + 2^2 + 7^2 + 7^2 and 1^3 + 4^3 + 5^3 + 8^3 = 702 = 2^3 + 2^3 + 7^3 + 7^3.
CROSSREFS
KEYWORD
hard,nonn,tabf
AUTHOR
Jonathan Sondow, Mar 10 2014
STATUS
approved