login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A261478 Number of set partitions of [n] such that no part contains two elements with a circular distance less than three. 2
1, 1, 1, 1, 1, 1, 8, 29, 106, 491, 2449, 12860, 72488, 435241, 2763053, 18485280, 129916333, 956237591, 7351602714, 58897588844, 490680801682, 4242904633903, 38014082900386, 352341757997443, 3373662297796822, 33326335447469262, 339232538360853201 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,7

COMMENTS

The circular distance of 1 and n is 1 (for n>1).

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..100

EXAMPLE

a(0) = 1: {}.

a(1) = 1: 1.

a(2) = 1: 1|2.

a(3) = 1: 1|2|3.

a(4) = 1: 1|2|3|4.

a(5) = 1: 1|2|3|4|5.

a(6) = 8: 14|25|36, 14|25|3|6, 14|2|36|5, 14|2|3|5|6, 1|25|36|4, 1|25|3|4|6, 1|2|36|4|5, 1|2|3|4|5|6.

a(7) = 29: 14|25|36|7, 14|25|37|6, 14|25|3|6|7, 14|26|37|5, 14|26|3|5|7, 14|2|36|5|7, 14|2|37|5|6, 14|2|3|5|6|7, 15|26|37|4, 15|26|3|47, 15|26|3|4|7, 15|2|36|47, 15|2|36|4|7, 15|2|37|4|6, 15|2|3|47|6, 15|2|3|4|6|7, 1|25|36|47, 1|25|36|4|7, 1|25|37|4|6, 1|25|3|47|6, 1|25|3|4|6|7, 1|26|37|4|5, 1|26|3|47|5, 1|26|3|4|5|7, 1|2|36|47|5, 1|2|36|4|5|7, 1|2|37|4|5|6, 1|2|3|47|5|6, 1|2|3|4|5|6|7.

MAPLE

b:= proc(n, l, m, h) option remember;

      `if`(n=0, `if`(1 in [l, m] or l=2, 0, 1), add(

      `if`(j in [l, m], 0, b(n-1, j, l, max(h, j))), j=1..h+1))

    end:

a:= n-> `if`(n<6, 1, b(n, 0$3)):

seq(a(n), n=0..30);

MATHEMATICA

b[n_, l_, m_, h_] := b[n, l, m, h] = If[n==0, If[l==1 || m==1 || l==2, 0, 1], Sum[If[j==l || j==m, 0, b[n - 1, j, l, Max[h, j]]], {j, 1, h + 1}]];

a[n_] := If[n < 6, 1, b[n, 0, 0, 0]];

a /@ Range[0, 30] (* Jean-Fran├žois Alcover, Dec 11 2020, after Alois P. Heinz *)

CROSSREFS

Row sums of A261477.

Sequence in context: A001360 A294838 A116952 * A199207 A088131 A072264

Adjacent sequences:  A261475 A261476 A261477 * A261479 A261480 A261481

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Aug 20 2015

STATUS

approved

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

License Agreements, Terms of Use, Privacy Policy. .

Last modified June 16 14:16 EDT 2021. Contains 345057 sequences. (Running on oeis4.)