The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A325105 Number of binary carry-connected subsets of {1...n}. 12
 1, 2, 3, 7, 8, 20, 48, 112, 113, 325, 777, 1737, 3709, 7741, 15869, 32253, 32254, 96538, 225798, 485702, 1006338, 2049602, 4137346, 8315266, 16697102, 33465934, 67007886, 134100366, 268301518, 536720590, 1073575118, 2147316942, 2147316943, 6441886323 (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. A subset is binary carry-connected if the graph whose vertices are the elements and whose edges are binary carries is connected. LINKS Alois P. Heinz, Table of n, a(n) for n = 0..1023 FORMULA a(n) = A306297(n,0) + A306297(n,1). - Alois P. Heinz, Mar 31 2019 EXAMPLE The a(0) = 1 through a(4) = 8 subsets: {} {} {} {} {} {1} {1} {1} {1} {2} {2} {2} {3} {3} {1,3} {4} {2,3} {1,3} {1,2,3} {2,3} {1,2,3} MAPLE h:= proc(n, s) local i, m; m:= n; for i in s do m:= Bits[Or](m, i) od; {m} end: g:= (n, s)-> (w-> `if`(w={}, s union {n}, s minus w union h(n, w)))(select(x-> Bits[And](n, x)>0, s)): b:= proc(n, s) option remember; `if`(n=0, `if`(nops(s)>1, 0, 1), b(n-1, s)+b(n-1, g(n, s))) end: a:= n-> b(n, {}): seq(a(n), n=0..35); # Alois P. Heinz, Mar 31 2019 MATHEMATICA binpos[n_]:=Join@@Position[Reverse[IntegerDigits[n, 2]], 1]; csm[s_]:=With[{c=Select[Tuples[Range[Length[s]], 2], And[OrderedQ[#], UnsameQ@@#, Length[Intersection@@s[[#]]]>0]&]}, If[c=={}, s, csm[Sort[Append[Delete[s, List/@c[[1]]], Union@@s[[c[[1]]]]]]]]]; Table[Length[Select[Subsets[Range[n]], Length[csm[binpos/@#]]<=1&]], {n, 0, 10}] CROSSREFS Cf. A019565, A080572, A247935, A304714, A304716, A305078. Cf. A325095, A325098, A325099, A325104, A325107, A325118, A325119. Partial sums of A306299. Sequence in context: A247843 A181658 A251541 * A276032 A114281 A137823 Adjacent sequences: A325102 A325103 A325104 * A325106 A325107 A325108 KEYWORD nonn AUTHOR Gus Wiseman, Mar 28 2019 EXTENSIONS a(16)-a(33) from Alois P. Heinz, Mar 31 2019 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified April 17 07:54 EDT 2024. Contains 371756 sequences. (Running on oeis4.)