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A271272 Number of set partitions of [n] into m blocks such that for each pair of distinct cyclically consecutive blocks (b,c) = (b,(b mod m)+1) at least one pair of numbers (i,j) = (i,(i mod n)+1) exists with i member of b and j member of c. 3
1, 1, 2, 5, 13, 36, 110, 374, 1404, 5750, 25419, 120325, 606210, 3234618, 18202851, 107647893, 666903189, 4316424771, 29116689197, 204259773724, 1487336089532, 11221857590608, 87591879539120, 706286859093554, 5875489876724901, 50364717424939105, 444367708336858660 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..26.

Wikipedia, Partition of a set

FORMULA

a(n) = A000110(n) - A271273(n).

EXAMPLE

A000110(4) - a(4) = 15 - 13 = 2: 13|2|4, 1|24|3.

A000110(5) - a(5) = 52 - 36 = 16: 124|3|5, 12|35|4, 134|2|5, 135|2|4, 13|25|4, 13|2|45, 13|2|4|5, 14|23|5, 1|235|4, 14|2|3|5, 15|24|3, 1|245|3, 1|24|3|5, 1|25|34, 1|25|3|4, 1|2|35|4.

MAPLE

b:= proc(n, i, m, l) option remember; `if`(n=0,

     `if`(l=[] or {l[]}={1} or i=m and {subsop(1=1, l)[]}=

      {1}, 1, 0), add(b(n-1, j, max(m, j), `if`(l=[], [1],

     `if`(j=m+1, subsop(1=0, `if`(j=i+1, [l[], 1], [l[], 0])),

     `if`(j=i+1 or j=1 and i=m, subsop(j=1, l), l)))), j=1..m+1))

    end:

a:= n-> b(n, 0$2, []):

seq(a(n), n=0..18);

MATHEMATICA

b[n_, i_, m_, l_] := b[n, i, m, l] = If[n==0, If[l=={} || Union[l]=={1} || i==m && Union @ ReplacePart[l, 1 -> 1] == {1}, 1, 0], Sum[b[n-1, j, Max[m, j], If[l=={}, {1}, If[j==m+1, ReplacePart[If[j==i+1, Append[l, 1], Append[l, 0]], 1 -> 0], If[j==i+1 || j==1 && i==m, ReplacePart[l, j -> 1], l]]]], {j, 1, m+1}]]; a[n_] := b[n, 0, 0, {}]; Table[a[n], {n, 0, 18} ] (* Jean-Fran├žois Alcover, Feb 15 2017, translated from Maple *)

CROSSREFS

Cf. A000110, A185983, A271270, A271273.

Sequence in context: A066723 A000994 A266546 * A148296 A148297 A148298

Adjacent sequences:  A271269 A271270 A271271 * A271273 A271274 A271275

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Apr 03 2016

STATUS

approved

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Last modified July 23 11:44 EDT 2019. Contains 325254 sequences. (Running on oeis4.)