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 A351874 Number of subsets of {1,2,...,n} such that any pair of elements do not differ by 1, 3, or 4. 1
 1, 2, 3, 5, 7, 9, 12, 16, 23, 33, 47, 66, 91, 126, 175, 245, 344, 482, 674, 940, 1311, 1830, 2557, 3575, 4997, 6982, 9752, 13620, 19025, 26579, 37136, 51885, 72487, 101264, 141463, 197624, 276088, 385711, 538860, 752810, 1051698, 1469249, 2052584, 2867532 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Table of n, a(n) for n=0..43. Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,1,0,1). FORMULA a(n) = a(n-1) + a(n-5) + a(n-7) + delta(n,0) + delta(n,1) + delta(n,2) + 2*delta(n,3) + 2*delta(n,4) + delta(n,5) + delta(n,6), a(n<0) = 0. G.f.: (1 + x + x^2 + 2*x^3 + 2*x^4 + x^5 + x^6)/(1 - x - x^5 - x^7). EXAMPLE When n = 5, the 9 subsets are {}, {1}, {2}, {3}, {4}, {5}, {1,3}, {2,4}, and {3,5}. MATHEMATICA CoefficientList[Series[(1 + x + x^2 + 2x^3 + 2x^4 + x^5 + x^6)/(1 - x - x^5 - x^7), {x, 0, 45}], x] CROSSREFS Other sequences giving numbers of restricted combinations: A000045, A006498, A006500, A031923, A000930, A130137, A263710, A079972, A224809, A351873, A224810, A224815, A003269, A317669, A177485, A121832, A224808, A003520, A224811, A005708, A224812, A005709, A224813, A005710. Sequence in context: A062438 A102424 A237826 * A080000 A333573 A361852 Adjacent sequences: A351871 A351872 A351873 * A351875 A351876 A351877 KEYWORD easy,nonn AUTHOR Michael A. Allen, Feb 22 2022 STATUS approved

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Last modified September 8 15:42 EDT 2024. Contains 375753 sequences. (Running on oeis4.)