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 A209436 Table of a(n,m) = number of subsets of {1,...,n} which contain two elements whose difference is m+1. 4
 0, 0, 0, 1, 0, 0, 3, 0, 0, 0, 8, 2, 0, 0, 0, 19, 7, 0, 0, 0, 0, 43, 17, 4, 0, 0, 0, 0, 94, 39, 14, 0, 0, 0, 0, 0, 201, 88, 37, 8, 0, 0, 0, 0, 0, 423, 192, 83, 28, 0, 0, 0, 0, 0, 0, 880, 408, 181, 74, 16, 0, 0, 0, 0, 0, 0, 1815, 855, 387, 175, 56, 0, 0, 0, 0 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,7 LINKS G. C. Greubel, Table of n, a(n) for the first 100 aintidiagonals, flattened M. Tetiva, Subsets that make no difference d, Mathematics Magazine 84 (2011), no. 4, 300-301. FORMULA a(n,m) = 2^n - Product_{i=0 to m} F(floor[(n + i)/(m + 1) + 2]) where F(n) is the n-th Fibonacci number. EXAMPLE Table begins: 0,   0,   0,   0,   0,   0,   0,   0,   0,   0, 0, ... 0,   0,   0,   0,   0,   0,   0,   0,   0,   0, 0, ... 1,   0,   0,   0,   0,   0,   0,   0,   0,   0, 0, ... 3,   2,   0,   0,   0,   0,   0,   0,   0,   0, 0, ... 8,   7,   4,   0,   0,   0,   0,   0,   0,   0, 0, ... 19,  17,  14,  8,   0,   0,   0,   0,   0,   0, 0, ... 43,  39,  37,  28,  16,  0,   0,   0,   0,   0, 0, ... 94,  88,  83,  74,  56,  32,  0,   0,   0,   0, 0, ... 201, 192, 181, 175, 148, 112, 64,  0,   0,   0, 0, ... 423, 408, 387, 377, 350, 296, 224, 128, 0,   0, 0, ... 880, 855, 824, 799, 781, 700, 592, 448, 256, 0, 0, ... ...................................................... a(3,1) 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 a(1,3) = 2. MATHEMATICA a[n_, m_] := 2^n - Product[Fibonacci[Floor[(n + i)/(m + 1) + 2]], {i, 0, m}]; Flatten[Table[a[j - i, i], {j, 0, 20}, {i, 0, j}]] CROSSREFS Cf. A209434, A209435, A209437. Sequence in context: A115859 A241663 A129170 * A229121 A190609 A325974 Adjacent sequences:  A209433 A209434 A209435 * A209437 A209438 A209439 KEYWORD nonn,tabl AUTHOR David Nacin, Mar 09 2012 STATUS approved

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Last modified October 23 22:08 EDT 2019. Contains 328373 sequences. (Running on oeis4.)