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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. 4
 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, 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, 16, 32, 48, 54, 75, 104, 144, 1, 2, 4, 8, 16, 32, 64, 72, 81 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS 1st row is the Fibonacci sequence. LINKS G. C. Greubel, Table of n, a(n) for the first 100 antidiagonals, flattened M. Tetiva, Subsets that make no difference d, Mathematics Magazine 84 (2011), no. 4, 300-301. FORMULA T(n,m) = Product_{i=0 to m} F(floor[(n + i)/(m + 1) + 2]) where F(n) is the n-th Fibonacci number. EXAMPLE Table begins: 1, 2, 3, 5,  8, 13, 21,  34,  55,  89,  144, ... 1, 2, 4, 6,  9, 15, 25,  40,  64, 104,  169, ... 1, 2, 4, 8, 12, 18, 27,  45,  75, 125,  200, ... 1, 2, 4, 8, 16, 24, 36,  54,  81, 135,  225, ... 1, 2, 4, 8, 16, 32, 48,  72, 108, 162,  243, ... 1, 2, 4, 8, 16, 32, 64,  96, 144, 216,  324, ... 1, 2, 4, 8, 16, 32, 64, 128, 192, 288,  432, ... 1, 2, 4, 8, 16, 32, 64, 128, 256, 384,  576, ... 1, 2, 4, 8, 16, 32, 64, 128, 256, 512,  768, ... 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, ... 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, ... ................................................ MATHEMATICA 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}]] CROSSREFS Cf. A209434, A209436, A209437. Sequence in context: A308500 A210950 A214314 * A263744 A268956 A208515 Adjacent sequences:  A209432 A209433 A209434 * A209436 A209437 A209438 KEYWORD nonn,tabl AUTHOR David Nacin, Mar 09 2012 STATUS approved

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Last modified October 23 17:32 EDT 2019. Contains 328373 sequences. (Running on oeis4.)