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Number of distinct n-row absolute difference tables that consist entirely of the first A000217(n) natural numbers.
1

%I #17 Apr 30 2014 01:34:22

%S 1,2,4,4,1

%N Number of distinct n-row absolute difference tables that consist entirely of the first A000217(n) natural numbers.

%C Mirror image triangle pairs are consider the same.

%D M. Gardner, "Pool-Ball Triangles", pp. 119-120 and 128, Penrose Tiles to Trapdoor Ciphers, Freeman NY 1989.

%D M. Gardner, Puzzles From Other Worlds, Problem 8, pp. 143; 173, Random House NY 1984.

%D J. D. E. Konhauser et al., " Difference triangles", Problem 145, pp. 43; 184-6, Which Way Did The Bicycle Go, MAA 1996.

%D P. Tougne, " Jeux Mathematiques", Aug. 1982 issue of Pour La Science (French edition of 'Scientific American'), Paris.

%H D. Greenwell, <a href="http://math2.eku.edu/greenwell/mat303/triangles/">Pool-ball Triangles</a>.

%H T. Sillke, <a href="http://www.mathematik.uni-bielefeld.de/~sillke/PUZZLES/triangle-abs-diff">Absolute-difference triangles</a>

%e Illustrating the case of the unique example of n=5 with numbers 1 through 15:

%e 6..14.15..3..13

%e ..8..1..12.10

%e ...7..11..2

%e ....4...9

%e ......5

%e For n=2 we have 1,3;2 and 2,3;1 so a(2) = 2. - _Michael Somos_, Apr 07 2012

%K nonn,fini

%O 1,2

%A _Lekraj Beedassy_, May 28 2004