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A274840 Number of set partitions of [n] such that the difference between each element and its block index is a multiple of seven. 2
1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 4, 5, 6, 7, 8, 17, 34, 65, 120, 215, 374, 629, 1641, 3919, 8849, 19241, 40707, 84203, 170229, 503902, 1407019, 3746718, 9600121, 23815820, 57408783, 134592586, 440661179, 1383544922, 4206645985, 12456581554, 36012285385 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,9

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..874

Wikipedia, Partition of a set

EXAMPLE

a(8) = 2: 18|2|3|4|5|6|7, 1|2|3|4|5|6|7|8.

a(9) = 3: 18|29|3|4|5|6|7, 1|29|3|4|5|6|7|8, 1|2|3|4|5|6|7|8|9.

a(10) = 4: 18|29|3(10)|4|5|6|7, 1|29|3(10)|4|5|6|7|8, 1|2|3(10)|4|5|6|7|8|9, 1|2|3|4|5|6|7|8|9|(10).

MAPLE

b:= proc(n, m, t) option remember; `if`(n=0, 1,

     add(`if`(irem(j-t, 7)=0, b(n-1, max(m, j),

              irem(t+1, 7)), 0), j=1..m+1))

    end:

a:= n-> b(n, 0, 1):

seq(a(n), n=0..42);

MATHEMATICA

b[n_, m_, t_] := b[n, m, t] = If[n == 0, 1, Sum[If[Mod[j - t, 7] == 0, b[n - 1, Max[m, j], Mod[t + 1, 7]], 0], {j, 1, m + 1}]];

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

Table[a[n], {n, 0, 42}] (* Jean-Fran├žois Alcover, May 15 2018, after Alois P. Heinz *)

CROSSREFS

Column k=7 of A274835.

Sequence in context: A146029 A140576 A200447 * A205406 A066759 A204928

Adjacent sequences:  A274837 A274838 A274839 * A274841 A274842 A274843

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Jul 08 2016

STATUS

approved

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Last modified May 22 08:21 EDT 2022. Contains 353933 sequences. (Running on oeis4.)