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 A357927 Number of subsets of [n] in which exactly half of the elements are Fibonacci numbers. 2
 1, 1, 1, 1, 4, 5, 15, 35, 56, 126, 252, 462, 792, 1716, 3003, 5005, 8008, 12376, 18564, 27132, 38760, 116280, 170544, 245157, 346104, 480700, 657800, 888030, 1184040, 1560780, 2035800, 2629575, 3365856, 4272048, 18156204, 23535820, 30260340, 38608020, 48903492 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 LINKS Alois P. Heinz, Table of n, a(n) for n = 0..10000 FORMULA a(n) = binomial(n,A072649(n)). a(n) = Sum_{j>=0} binomial(A072649(n),j)*binomial(n-A072649(n),j). EXAMPLE a(6) = 15: {}, {1,4}, {1,6}, {2,4}, {2,6}, {3,4}, {3,6}, {4,5}, {5,6}, {1,2,4,6}, {1,3,4,6}, {1,4,5,6}, {2,3,4,6}, {2,4,5,6}, {3,4,5,6}. MAPLE f:= proc(n) option remember; `if`(n=0, 0, f(n-1)+ `if`((t-> ormap(issqr, [t-4, t+4]))(5*n^2), 1, 0)) end: a:= n-> binomial(n, f(n)): seq(a(n), n=0..38); MATHEMATICA f[n_] := Module[{j}, For[j = Floor@Log[GoldenRatio, n], Fibonacci[j+1] <= n, j++]; j-1]; a[n_] := If[n == 0, 1, Binomial[n, f[n]]]; Table[a[n], {n, 0, 38}] (* Jean-François Alcover, Nov 17 2022 *) CROSSREFS Cf. A000045, A037031, A072649, A102366, A180272, A357812. Sequence in context: A006491 A321174 A304921 * A051721 A050226 A119562 Adjacent sequences: A357924 A357925 A357926 * A357928 A357929 A357930 KEYWORD nonn AUTHOR Alois P. Heinz, Oct 20 2022 STATUS approved

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Last modified August 5 15:49 EDT 2024. Contains 374950 sequences. (Running on oeis4.)