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 A324172 Number of subsets of {1,...,n} that cross their complement. 17
 0, 0, 0, 0, 2, 10, 32, 84, 198, 438, 932, 1936, 3962, 8034, 16200, 32556, 65294, 130798, 261836, 523944, 1048194, 2096730, 4193840, 8388100, 16776662, 33553830, 67108212, 134217024, 268434698, 536870098, 1073740952, 2147482716, 4294966302, 8589933534, 17179868060 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS Two sets cross each other if they are of the form {{...x...y...}, {...z...t...}} where x < z < y < t or z < x < t < y. LINKS Colin Barker, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (5,-9,7,-2). FORMULA a(0) = 0; a(n) = 2^n - n^2 + n - 2. a(n) = 2*A002662(n-1) for n > 0. G.f.: 2*x^4/((1-2*x)*(1-x)^3). a(n) = 5*a(n-1) - 9*a(n-2) + 7*a(n-3) - 2*a(n-4) for n>4. - Colin Barker, Feb 18 2019 EXAMPLE The a(5) = 10 subsets are {1,3}, {1,4}, {2,4}, {2,5}, {3,5}, {1,2,4}, {1,3,4}, {1,3,5}, {2,3,5}, {2,4,5}. MATHEMATICA croXQ[stn_]:=MatchQ[stn, {___, {___, x_, ___, y_, ___}, ___, {___, z_, ___, t_, ___}, ___}/; x

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Last modified April 10 16:05 EDT 2021. Contains 342845 sequences. (Running on oeis4.)