OFFSET
0,29
COMMENTS
If n is a triangular number (A000217), then there is a trivial solution using piles of 1,2,3,...,k, where n = k(k+1)/2. All solutions are based on sums of triangular numbers, but not all such sums are legal. No indices of the triangular numbers can have a ratio smaller than 2; if they do then labels from the two triangles are not disjoint. a(28) = 2 because we can either use the trivial T(7) = 28 solution or the T(6) + T(3) + T(1) = 21 + 6 + 1 = 28 solution. A093579 gives the integers for which there is a solution and A093580 those for which there is no solution, so that a(A093579(n)) > 0 and a(A093580(n)) = 0 for all n.
EXAMPLE
a(1) = 1 because the only possible label is (1,1); a(2) = 0 because there is no way to prevent both pieces of paper from getting labeled identically.
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Howard A. Landman, Apr 01 2004
STATUS
approved