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

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A239510 Number of partitions p of n such that if h = min(p), then h is an (h,0)-separator of p; see Comments. 4

%I #8 Jan 28 2022 01:01:17

%S 0,0,0,0,1,1,2,4,5,7,11,13,18,24,30,37,48,59,73,90,109,132,163,193,

%T 233,280,334,397,475,559,663,784,924,1085,1279,1494,1751,2049,2392,

%U 2784,3248,3769,4382,5081,5887,6808,7879,9087,10486,12083,13910,15988,18384

%N Number of partitions p of n such that if h = min(p), then h is an (h,0)-separator of p; see Comments.

%C Suppose that p is a partition of n into 2 or more parts and that h is a part of p. Then p is (h,0)-separable if there is an ordering x, h, x, h, ..., h, x of the parts of p, where each x represents any part of p except h. Here, the number of h's on the ends of the ordering is 0. Similarly, p is (h,1)-separable if there is an ordering x, h, x, h, ..., x, h, where the number of h's on the ends is 1; next, p is (h,2)-separable if there is an ordering h, x, h, ..., x, h. Finally, p is h-separable if it is (h,i)-separable for i = 0,1,2.

%e a(9) counts these 5 partitions: 612, 513, 414, 423, 312121.

%t z = 75; Table[Count[IntegerPartitions[n], p_ /; 2 Count[p, Min[p]] == Length[p] - 1], {n, 1, z}] (* A239510 *)

%t Table[Count[IntegerPartitions[n], p_ /; 2 Count[p, 2 Min[p]] == Length[p] - 1], {n, 1, z}] (* A239511 *)

%t Table[Count[IntegerPartitions[n], p_ /; 2 Count[p, Max[p]] == Length[p] - 1], {n, 1, z}] (* A237828 *)

%t Table[Count[Rest[IntegerPartitions[n]], p_ /; 2 Count[p, Length[p]] == Length[p] - 1], {n, 1, z}] (* A239513 *)

%t Table[Count[Rest[IntegerPartitions[n]], p_ /; 2 Count[p, Max[p] - Min[p]] == Length[p] - 1], {n, 1, z}] (* A239514 *)

%Y Cf. A239511, A237828, A239513, A239514, A239482.

%K nonn,easy

%O 1,7

%A _Clark Kimberling_, Mar 24 2014

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.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 28 04:13 EDT 2024. Contains 371235 sequences. (Running on oeis4.)