A036818 - OEIS

%I #12 Jul 08 2024 03:03:09

%S 0,1,1,1,2,2,3,4,4,8,6,11,12,14,22,21,30,36,39,59,57,80,92,105,142,

%T 148,193,225,252,334,349,447,513,582,735,793,977,1126,1269,1573,1702,

%U 2071,2363,2673,3233,3541,4221,4816,5421,6474,7104,8382,9505,10705,12592,13888,16185,18317,20557,23966

%N Number of partitions satisfying (cn(0,5) = 0 and cn(1,5) = cn(4,5)).

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

%C Short: (0 := 0 and 1=4).

%p c := proc(L,i,n)

%p     option remember;

%p     local a,p;

%p     a := 0 ;

%p     for p in L do

%p         if modp(p,n) = i then

%p             a := a+1 ;

%p         end if;

%p     end do:

%p     a ;

%p end proc:

%p A036818 := proc(n)

%p     local a ;

%p     a := 0 ;

%p     for p in combinat[partition](n) do

%p         if c(p,0,5) = 0 then

%p             if c(p,1,5) = c(p,4,5) then

%p                 a := a+1 ;

%p             end if;

%p         end if;

%p     end do:

%p     a ;

%p end proc:

%p for n from 1 do

%p     print(n,A036818(n)) ;

%p end do: # _R. J. Mathar_, Oct 19 2014

%t c[L_, i_, n_]  := c[L, i, n] = Module[{a = 0},

%t    Do[If[Mod[p, n] == i, a++], {p, L}]; a];

%t A036818[n_] := A036818[n] = Module[{a = 0},

%t    Do[If[c[p, 0, 5] == 0, If[c[p, 1, 5] == c[p, 4, 5], a++]],

%t    {p, IntegerPartitions[n]}]; a];

%t Table[Print[n, " ", A036818[n]]; A036818[n], {n, 1, 60}] (* _Jean-François Alcover_, Jul 08 2024, after _R. J. Mathar_ *)

%K nonn

%O 1,5

%A _Olivier Gérard_

%E a(48)-a(60) from _Jean-François Alcover_, Jul 08 2024