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 A209439 Table T(n,d) where T(n,d) gives the number of subsets of length n that do not contain an arithmetic progression of length 3 with distance d. 4
 1, 2, 1, 4, 2, 1, 7, 4, 2, 1, 13, 8, 4, 2, 1, 24, 16, 8, 4, 2, 1, 44, 28, 16, 8, 4, 2, 1, 81, 49, 32, 16, 8, 4, 2, 1, 149, 91, 64, 32, 16, 8, 4, 2, 1, 274, 169, 112, 64, 32, 16, 8, 4, 2, 1, 504, 312, 196, 128, 64, 32, 16, 8, 4, 2, 1, 927, 576, 343, 256, 128 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS First column just gives the tribonacci numbers. n offset is zero, but d offset is one so 1st entry is a(0,1). LINKS G. C. Greubel, Table of n, a(n) for the first 25 rows, flattened FORMULA T(n,d) = Product_{i=0..d-1} Tr(floor(n + i)/d) + 2) where Tr(n) is the n-th tribonacci number. EXAMPLE 1,   1,   1,   1,    1,    1,    1,    1,    1,    1 ...     2,   2,   2,   2,    2,    2,    2,    2,    2,    2 ...     4,   4,   4,   4,    4,    4,    4,    4,    4,    4 ...     7,   8,   8,   8,    8,    8,    8,    8,    8,    8 ...    13,  16,  16,  16,   16,   16,   16,   16,   16,   16 ...    24,  28,  32,  32,   32,   32,   32,   32,   32,   32 ...    44,  49,  64,  64,   64,   64,   64,   64,   64,   64 ...    81,  91, 112, 128,  128,  128,  128,  128,  128,  128 ...   149, 169, 196, 256,  256,  256,  256,  256,  256,  256 ...   274, 312, 343, 448,  512,  512,  512,  512,  512,  512 ...   504, 576, 637, 784, 1024, 1024, 1024, 1024, 1024, 1024 ... ............................................................ For a(5,2) we count subsets of {1,...,5} that do not contain {1,3,5}, the only d=2 AP possible here.  There are 4 subsets containing {1,3,5} so a(5,2) = 2^5-4 = 28. MATHEMATICA Trib[0] = 0; Trib[1] = 1; Trib[2] = 1; Trib[n_] := Trib[n - 1] + Trib[n - 2] + Trib[n - 3]; T[n_, d_] := Product[Trib[Floor[(n + i)/d] + 2], {i, 0, d - 1}]; Flatten[Table[T[j - i, i + 1], {j, 0, 15}, {i, 0, j}]] CROSSREFS Cf. A209438, A209490, A209491. Sequence in context: A165899 A316354 A104582 * A133938 A239829 A210034 Adjacent sequences:  A209436 A209437 A209438 * A209440 A209441 A209442 KEYWORD nonn,tabl AUTHOR David Nacin, Mar 09 2012 STATUS approved

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Last modified November 15 04:00 EST 2018. Contains 317225 sequences. (Running on oeis4.)