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%I #24 Jan 03 2018 15:56:55
%S 1,1,2,1,2,3,1,2,4,5,1,2,4,6,8,1,2,4,8,9,13,1,2,4,8,12,15,21,1,2,4,8,
%T 16,18,25,34,1,2,4,8,16,24,27,40,55,1,2,4,8,16,32,36,45,64,89,1,2,4,8,
%U 16,32,48,54,75,104,144,1,2,4,8,16,32,64,72,81
%N Table T(m,n), read by antidiagonals, is the number of subsets of {1,...,n} which do not contain two elements whose difference is m+1.
%C 1st row is the Fibonacci sequence.
%H G. C. Greubel, <a href="/A209435/b209435.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(n,m) = Product_{i=0 to m} F(floor[(n + i)/(m + 1) + 2]) where F(n) is the n-th Fibonacci number.
%e Table begins:
%e 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, ...
%e 1, 2, 4, 6, 9, 15, 25, 40, 64, 104, 169, ...
%e 1, 2, 4, 8, 12, 18, 27, 45, 75, 125, 200, ...
%e 1, 2, 4, 8, 16, 24, 36, 54, 81, 135, 225, ...
%e 1, 2, 4, 8, 16, 32, 48, 72, 108, 162, 243, ...
%e 1, 2, 4, 8, 16, 32, 64, 96, 144, 216, 324, ...
%e 1, 2, 4, 8, 16, 32, 64, 128, 192, 288, 432, ...
%e 1, 2, 4, 8, 16, 32, 64, 128, 256, 384, 576, ...
%e 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 768, ...
%e 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, ...
%e 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, ...
%e ................................................
%t a[n_, m_] := Product[Fibonacci[Floor[(n + i)/(m + 1) + 2]], {i, 0, m}]; Flatten[Table[a[i, j - i], {i, 0, 30}, {j, 0, i}]]
%Y Cf. A209434, A209436, A209437.
%K nonn,tabl
%O 0,3
%A _David Nacin_, Mar 09 2012
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