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 A325095 Number of subsets of {1...n} with no binary carries. 13
 1, 2, 4, 5, 10, 12, 14, 15, 30, 35, 40, 42, 47, 49, 51, 52, 104, 119, 134, 139, 154, 159, 164, 166, 181, 186, 191, 193, 198, 200, 202, 203, 406, 458, 510, 525, 577, 592, 607, 612, 664, 679, 694, 699, 714, 719, 724, 726, 778, 793, 808, 813, 828, 833, 838, 840 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS A binary carry of two positive integers is an overlap of the positions of 1's in their reversed binary expansion. For example, the binary representations of {2,5,8} are: 2 = 10, 5 = 101, 8 = 1000, and since there are no columns with more than one 1, {2,5,8} is counted under a(8). LINKS Alois P. Heinz, Table of n, a(n) for n = 0..16383 FORMULA a(2^n - 1) = A000110(n + 1). EXAMPLE The a(1) = 1 through a(7) = 15 subsets: {} {} {} {} {} {} {} {1} {1} {1} {1} {1} {1} {1} {2} {2} {2} {2} {2} {2} {1,2} {3} {3} {3} {3} {3} {1,2} {4} {4} {4} {4} {1,2} {5} {5} {5} {1,4} {1,2} {6} {6} {2,4} {1,4} {1,2} {7} {3,4} {2,4} {1,4} {1,2} {1,2,4} {2,5} {1,6} {1,4} {3,4} {2,4} {1,6} {1,2,4} {2,5} {2,4} {3,4} {2,5} {1,2,4} {3,4} {1,2,4} MAPLE b:= proc(n, t) option remember; `if`(n=0, 1, b(n-1, t)+ `if`(Bits[And](n, t)=0, b(n-1, Bits[Or](n, t)), 0)) end: a:= n-> b(n, 0): seq(a(n), n=0..63); # Alois P. Heinz, Mar 28 2019 MATHEMATICA binpos[n_]:=Join@@Position[Reverse[IntegerDigits[n, 2]], 1]; stableQ[u_, Q_]:=!Apply[Or, Outer[#1=!=#2&&Q[#1, #2]&, u, u, 1], {0, 1}]; Table[Length[Select[Subsets[Range[n]], stableQ[#, Intersection[binpos[#1], binpos[#2]]!={}&]&]], {n, 0, 10}] CROSSREFS Cf. A000110, A019565, A050315, A080572, A247935, A267610, A267700. Cf. A325094, A325096, A325097, A325100, A325103, A325104, A325105. Sequence in context: A241268 A285697 A047611 * A120491 A177186 A260385 Adjacent sequences: A325092 A325093 A325094 * A325096 A325097 A325098 KEYWORD nonn,look AUTHOR Gus Wiseman, Mar 27 2019 EXTENSIONS a(16)-a(55) from Alois P. Heinz, Mar 28 2019 STATUS approved

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Last modified February 27 14:46 EST 2024. Contains 370376 sequences. (Running on oeis4.)