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

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A241316 Number of partitions p of n into distinct parts, including round(mean(p)). 6
 0, 1, 1, 2, 1, 2, 2, 3, 2, 4, 4, 5, 5, 7, 7, 10, 10, 13, 15, 17, 19, 25, 27, 31, 35, 44, 49, 59, 63, 74, 85, 99, 114, 126, 143, 166, 189, 221, 242, 277, 306, 351, 404, 447, 506, 565, 623, 710, 791, 899, 1021, 1150, 1268, 1364, 1533, 1734, 1949, 2149, 2386 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 LINKS FORMULA a(n) + A241317(n) = A000009(n) for n >= 1. EXAMPLE a(10) counts these 4 partitions:  {10,}, {5,4,1}, {5,3,2}, {4,3,2,1}. MATHEMATICA z = 30; f[n_] := f[n] = Select[IntegerPartitions[n], Max[Length /@ Split@#] == 1 &];     Table[Count[f[n], p_ /; MemberQ[p, Floor[Mean[p]]]], {n, 0, z}] (* A241312 *)     Table[Count[f[n], p_ /; ! MemberQ[p, Floor[Mean[p]]]], {n, 0, z}] (* A241313 *)     Table[Count[f[n], p_ /; MemberQ[p, Ceiling[Mean[p]]]], {n, 0, z}] (* A241314 *)     Table[Count[f[n], p_ /; ! MemberQ[p, Ceiling[Mean[p]]]], {n, 0, z}] (* A241315 *)     Table[Count[f[n], p_ /; MemberQ[p, Round[Mean[p]]]], {n, 0, z}] (* A241316 *)     Table[Count[f[n], p_ /; ! MemberQ[p, Round[Mean[p]]]], {n, 0, ] (* A241317 *) CROSSREFS Cf. A241317, A241318, A000009. Sequence in context: A127685 A127687 A024156 * A241312 A075989 A304714 Adjacent sequences:  A241313 A241314 A241315 * A241317 A241318 A241319 KEYWORD nonn,easy AUTHOR Clark Kimberling, Apr 19 2014 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 August 13 14:01 EDT 2022. Contains 356091 sequences. (Running on oeis4.)