A036818 Number of partitions satisfying (cn(0,5) = 0 and cn(1,5) = cn(4,5)).

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, 148, 193, 225, 252, 334, 349, 447, 513, 582, 735, 793, 977, 1126, 1269, 1573, 1702, 2071, 2363, 2673, 3233, 3541, 4221, 4816, 5421, 6474, 7104, 8382, 9505, 10705, 12592, 13888, 16185, 18317, 20557, 23966

Offset

1,5

Comments

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

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

Links

Table of n, a(n) for n=1..60.

Maple

c := proc(L, i, n)
    option remember;
    local a, p;
    a := 0 ;
    for p in L do
        if modp(p, n) = i then
            a := a+1 ;
        end if;
    end do:
    a ;
end proc:
A036818 := proc(n)
    local a ;
    a := 0 ;
    for p in combinat[partition](n) do
        if c(p, 0, 5) = 0 then
            if c(p, 1, 5) = c(p, 4, 5) then
                a := a+1 ;
            end if;
        end if;
    end do:
    a ;
end proc:
for n from 1 do
    print(n, A036818(n)) ;
end do: # R. J. Mathar, Oct 19 2014

Mathematica

c[L_, i_, n_]  := c[L, i, n] = Module[{a = 0},
   Do[If[Mod[p, n] == i, a++], {p, L}]; a];
A036818[n_] := A036818[n] = Module[{a = 0},
   Do[If[c[p, 0, 5] == 0, If[c[p, 1, 5] == c[p, 4, 5], a++]],
   {p, IntegerPartitions[n]}]; a];
Table[Print[n, " ", A036818[n]]; A036818[n], {n, 1, 60}] (* Jean-François Alcover, Jul 08 2024, after R. J. Mathar *)

Crossrefs

Sequence in context: A153937 A357710 A242971 * A036813 A036814 A137776

Adjacent sequences: A036815 A036816 A036817 * A036819 A036820 A036821

Keyword

nonn

Author

Olivier Gérard

Extensions

a(48)-a(60) from Jean-François Alcover, Jul 08 2024

Status

approved