p:=proc(n)
  option remember;
  local k,s:=0,m;
  for k from 1 while (m:=iquo(k*(3*k-1),2))<=n do
    s-=(-1)^k*p(n-m);
  od;
  for k from 1 while (m:=iquo(k*(3*k+1),2))<=n do
    s-=(-1)^k*p(n-m);
  od;
  s
end:
p(0):=1:

time(p(6666));
# 0.796

time(combinat[numbpart](6666));
# 0.406

p~([$1..20]);
# [1, 2, 3, 5, 7, 11, 15, 22, 30, 42, 56, 77, 101, 135, 176, 231, 297, 385, 490, 627]

combinat[numbpart]~([$1..20]);
# [1, 2, 3, 5, 7, 11, 15, 22, 30, 42, 56, 77, 101, 135, 176, 231, 297, 385, 490, 627]

p(1000)
# 24061467864032622473692149727991

combinat[numbpart](1000);
# 24061467864032622473692149727991