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A209435 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.

%I A209435 #24 Jan 03 2018 15:56:55
%S A209435 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 A209435 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 A209435 16,32,48,54,75,104,144,1,2,4,8,16,32,64,72,81
%N A209435 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 A209435 1st row is the Fibonacci sequence.
%H A209435 G. C. Greubel, <a href="/A209435/b209435.txt">Table of n, a(n) for the first 100 antidiagonals, flattened</a>
%H A209435 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 A209435 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 A209435 Table begins:
%e A209435 1, 2, 3, 5,  8, 13, 21,  34,  55,  89,  144, ...
%e A209435 1, 2, 4, 6,  9, 15, 25,  40,  64, 104,  169, ...
%e A209435 1, 2, 4, 8, 12, 18, 27,  45,  75, 125,  200, ...
%e A209435 1, 2, 4, 8, 16, 24, 36,  54,  81, 135,  225, ...
%e A209435 1, 2, 4, 8, 16, 32, 48,  72, 108, 162,  243, ...
%e A209435 1, 2, 4, 8, 16, 32, 64,  96, 144, 216,  324, ...
%e A209435 1, 2, 4, 8, 16, 32, 64, 128, 192, 288,  432, ...
%e A209435 1, 2, 4, 8, 16, 32, 64, 128, 256, 384,  576, ...
%e A209435 1, 2, 4, 8, 16, 32, 64, 128, 256, 512,  768, ...
%e A209435 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, ...
%e A209435 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, ...
%e A209435 ................................................
%t A209435 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 A209435 Cf. A209434, A209436, A209437.
%K A209435 nonn,tabl
%O A209435 0,3
%A A209435 _David Nacin_, Mar 09 2012