OFFSET
0,6
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..768
Wikipedia, Partition of a set
EXAMPLE
a(7) = 4: 15|26|37|4, 1|26|37|4|5, 1|2|37|4|5|6, 1|2|3|4|5|6|7.
a(8) = 5: 15|26|37|48, 1|26|37|48|5, 1|2|37|48|5|6, 1|2|3|48|5|6|7, 1|2|3|4|5|6|7|8.
a(9) = 11: 159|26|37|48, 15|26|37|48|9, 19|26|37|48|5, 1|26|37|48|59, 19|2|37|48|5|6, 1|2|37|48|59|6, 19|2|3|48|5|6|7, 1|2|3|48|59|6|7, 19|2|3|4|5|6|7|8, 1|2|3|4|59|6|7|8, 1|2|3|4|5|6|7|8|9.
MAPLE
b:= proc(n, m, t) option remember; `if`(n=0, 1,
add(`if`(irem(j-t, 4)=0, b(n-1, max(m, j),
irem(t+1, 4)), 0), j=1..m+1))
end:
a:= n-> b(n, 0, 1):
seq(a(n), n=0..35);
MATHEMATICA
b[n_, m_, t_] := b[n, m, t] = If[n == 0, 1, Sum[If[Mod[j - t, 4] == 0, b[n - 1, Max[m, j], Mod[t + 1, 4]], 0], {j, 1, m + 1}]];
a[n_] := b[n, 0, 1];
Table[a[n], {n, 0, 35}] (* Jean-François Alcover, May 15 2018, after Alois P. Heinz *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Jul 08 2016
STATUS
approved