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 A096202 Number of coverings of {1...n} by translation of a single set. 4
 1, 2, 3, 6, 11, 22, 45, 92, 188, 382, 791, 1632, 3357, 6922, 14289, 29542, 61013, 126142, 260664, 538850, 1113372, 2300954, 4752279, 9814226, 20257082, 41798206, 86204773, 177729712, 366231907, 754356336, 1553063269, 3196028942, 6573883225, 13515943986, 27775807554 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS The number of sets (up to translation) that with their translations can cover {1...n} in at least one way is given by A079500(n). For example, for n = 5 the 8 sets are {1}, {1,2}, {1,3}, {1,2,3}, {1,2,4}, {1,3,4}, {1,2,3,4}, {1,2,3,4,5}. - Andrew Howroyd, Nov 06 2019 LINKS Table of n, a(n) for n=1..35. EXAMPLE a(5)=11 because the following are the 11 coverings of {1...5}, each one of which only uses a single set and its translations: {{1},{2},{3},{4},{5}} {{1,2},{3,4},{4,5}} {{1,2},{2,3},{3,4},{4,5}} {{1,2},{2,3},{4,5}} {{1,3},{2,4},{3,5}} {{1,2,3},{2,3,4},{3,4,5}} {{1,2,3},{3,4,5}} {{1,2,4},{2,3,5}} {{1,3,4},{2,4,5}} {{1,2,3,4},{2,3,4,5}} {{1,2,3,4,5}} PROG (PARI) covers(all, v)={ my(u=vector(#v+1)); for(i=1, #v, u[i+1]=bitor(u[i], v[i])); my(recurse(k, b) = if(bitnegimply(b, u[k+1]), 0, if(k==0, 1, my(t=bitnegimply(b, v[k])); if(t==b, 2*self()(k-1, b), self()(k-1, b) + self()(k-1, t)) ))); recurse(#v, all) } a(n)={sum(i=2^(n-1), 2^n-1, covers(2^n-1, vector(valuation(i, 2)+1, j, i>>(j-1))))} \\ Andrew Howroyd, Nov 06 2019 CROSSREFS Cf. A079500, A096154, A096203. Sequence in context: A007477 A274936 A244521 * A036653 A318031 A316500 Adjacent sequences: A096199 A096200 A096201 * A096203 A096204 A096205 KEYWORD nonn AUTHOR Jon Wild, Jul 27 2004 EXTENSIONS a(14)-a(32) from Andrew Howroyd, Nov 06 2019 a(33)-a(35) from Jinyuan Wang, Jun 09 2021 STATUS approved

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Last modified June 8 18:04 EDT 2023. Contains 363165 sequences. (Running on oeis4.)