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 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-François 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

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