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A274843
Number of set partitions of [n] such that the difference between each element and its block index is a multiple of ten.
2
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 23, 46, 89, 168, 311, 566, 1013, 1780, 3059, 5106, 13283, 31683, 71545, 155833, 331139, 691387, 1424525, 2902605, 5848135, 11610871, 34108236, 95170569, 254432006, 657159051, 1650540916
OFFSET
0,12
LINKS
EXAMPLE
a(10) = 1: 1|2|3|4|5|6|7|8|9|(10).
a(11) = 2: 1(11)|2|3|4|5|6|7|8|9|(10), 1|2|3|4|5|6|7|8|9|(10)|(11).
MAPLE
b:= proc(n, m, t) option remember; `if`(n=0, 1,
add(`if`(irem(j-t, 10)=0, b(n-1, max(m, j),
irem(t+1, 10)), 0), j=1..m+1))
end:
a:= n-> b(n, 0, 1):
seq(a(n), n=0..50);
MATHEMATICA
b[n_, m_, t_] := b[n, m, t] = If[n == 0, 1, Sum[If[Mod[j - t, 10] == 0, b[n - 1, Max[m, j], Mod[t + 1, 10]], 0], {j, 1, m + 1}]];
a[n_] := b[n, 0, 1];
Table[a[n], {n, 0, 50}] (* Jean-François Alcover, May 15 2018, after Alois P. Heinz *)
CROSSREFS
Column k=10 of A274835.
Sequence in context: A179309 A032946 A273738 * A039156 A132030 A288327
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Jul 08 2016
STATUS
approved