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 A324172 Number of subsets of {1,...,n} that cross their complement. 18
 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. Also the number of verex cuts in the wheel graph on n nodes. - Eric W. Weisstein, Apr 22 2023 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). Eric Weisstein's World of Mathematics, Vertex Cut Eric Weisstein's World of Mathematics, Wheel Graph 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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