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%I #31 Jan 03 2018 15:57:40
%S 1,0,3,0,2,8,0,0,7,19,0,0,4,17,43,0,0,0,14,39,94,0,0,0,8,37,88,201,0,
%T 0,0,0,28,83,192,423,0,0,0,0,16,74,181,408,880,0,0,0,0,0,56,175,387,
%U 855,1815,0,0,0,0,0,32,148,377,824,1775,3719,0,0,0,0,0
%N Table of T(m,n), read by antidiagonals, is the number of subsets of {1,...,n} which contain two elements whose difference is m.
%C m offset is 1, n offset is 2 so 1st entry is T(1,2).
%H G. C. Greubel, <a href="/A209437/b209437.txt">Table of n, a(n) for the first 100 antidiagonals, flattened</a>
%H M. Tetiva, <a href="http://www.jstor.org/stable/10.4169/math.mag.84.4.296">Subsets that make no difference d</a>, Mathematics Magazine 84 (2011), no. 4, 300-301.
%F T(m,n) = 2^n - Product_{i=0,...,m-1} F(floor((n + i)/m + 2)) where F(n) is the n-th Fibonacci number.
%e Table begins:
%e 1, 3, 8, 19, 43, 94, 201, 423, 880, ...
%e 0, 2, 7, 17, 39, 88, 192, 408, 855, ...
%e 0, 0, 4, 14, 37, 83, 181, 387, 824, ...
%e 0, 0, 0, 8, 28, 74, 175, 377, 799, ...
%e 0, 0, 0, 0, 16, 56, 148, 350, 781, ...
%e 0, 0, 0, 0, 0, 32, 112, 296, 700, ...
%e 0, 0, 0, 0, 0, 0, 64, 224, 592, ...
%e 0, 0, 0, 0, 0, 0, 0, 128, 448, ...
%e 0, 0, 0, 0, 0, 0, 0, 0, 256, ...
%e 0, 0, 0, 0, 0, 0, 0, 0, 0, ...
%e 0, 0, 0, 0, 0, 0, 0, 0, 0, ...
%e .......................................
%e T(2,3) is the number of subsets of {1,2,3} containing two elements whose difference is two. There are 2 of these: {1,3} and {1,2,3} so T(2,3) = 2.
%t T[m_, n_] := 2^n - Product[Fibonacci[Floor[(n + i)/m + 2]], {i, 0, m - 1}]; Table[T[i, j + 2], {i, 1, 10}, {j, 0, 10}]; Flatten[Table[T[i - j + 1, j + 2], {i, 0, 20}, {j, 0, i}]]
%Y Cf. A209434, A209435, A209436.
%K nonn,tabl
%O 1,3
%A _David Nacin_, Mar 09 2012
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