A039902 - OEIS

%I #14 Nov 12 2015 06:06:02

%S 0,1,1,2,4,6,9,13,19,27,39,52,71,95,127,170,220,286,371,474,614,770,

%T 979,1229,1541,1934,2392,2968,3668,4504,5556,6764,8271,10055,12199,

%U 14798,17836,21504,25860,30996,37185,44348,52943,63003,74856,88874,105165,124376

%N Number of partitions satisfying 0 < cn(1,5) + cn(4,5) + cn(2,5) and 0 < cn(1,5) + cn(4,5) + cn(3,5).

%C For a given partition cn(i,n) means the number of its parts equal to i modulo n.

%C Short: o < 1 + 4 + 2 and o < 1 + 4 + 3 (OMBBAAp).

%H Alois P. Heinz, <a href="/A039902/b039902.txt">Table of n, a(n) for n = 0..1000</a>

%p b:= proc(n, i, t, s) option remember; `if`(n=0, t*s,

%p       `if`(i<1, 0, b(n, i-1, t, s)+ `if`(i>n, 0,

%p        b(n-i, i, `if`(irem(i, 5) in {0, 3}, t, 1),

%p       `if`(irem(i, 5) in {0, 2}, s, 1)))))

%p     end:

%p a:= n-> b(n$2, 0$2):

%p seq(a(n), n=0..50);  # _Alois P. Heinz_, Apr 04 2014

%t 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_ *)

%K nonn

%O 0,4

%A _Olivier Gérard_