OFFSET
0,4
COMMENTS
For a given partition cn(i,n) means the number of its parts equal to i modulo n.
Short: o < 1 + 4 + 2 and o < 1 + 4 + 3 (OMBBAAp).
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..1000
MAPLE
b:= proc(n, i, t, s) option remember; `if`(n=0, t*s,
`if`(i<1, 0, b(n, i-1, t, s)+ `if`(i>n, 0,
b(n-i, i, `if`(irem(i, 5) in {0, 3}, t, 1),
`if`(irem(i, 5) in {0, 2}, s, 1)))))
end:
a:= n-> b(n$2, 0$2):
seq(a(n), n=0..50); # Alois P. Heinz, Apr 04 2014
MATHEMATICA
b[n_, i_, t_, s_] := b[n, i, t, s] = If[n == 0, t*s, If[i<1, 0, b[n, i-1, t, s] + If[i>n, 0, b[n-i, i, If[MemberQ[{0, 3}, Mod[i, 5] ], t, 1], If[MemberQ[{0, 2}, Mod[i, 5]], s, 1]]]]]; a[n_] := b[n, n, 0, 0]; Table[a[n], {n, 0, 50}] (* Jean-François Alcover, Nov 12 2015, after Alois P. Heinz *)
CROSSREFS
KEYWORD
nonn
AUTHOR
STATUS
approved