cp's OEIS Frontend

A036822 Number of partitions satisfying cn(1,5) = cn(4,5) = 0.

%I A036822 #31 Aug 10 2020 08:44:05
%S A036822 0,1,1,1,2,2,3,4,4,7,6,10,11,13,18,19,25,30,33,45,47,61,70,81,100,111,
%T A036822 135,157,177,218,238,288,328,374,443,495,579,663,747,878,973,1134,
%U A036822 1281,1448,1670,1863,2135,2414,2705,3103
%N A036822 Number of partitions satisfying cn(1,5) = cn(4,5) = 0.
%C A036822 For a given partition cn(i,n) means the number of its parts equal to i modulo n.
%C A036822 Short: (1=4 := 0).
%C A036822 a(n) is the number of partitions with parts congruent to 0, 2 or 3 mod 5. - _George Beck_, Aug 08 2020
%H A036822 Jinyuan Wang, <a href="/A036822/b036822.txt">Table of n, a(n) for n = 1..1000</a>
%F A036822 Convolution inverse of A113428. - _George Beck_, May 21 2016
%F A036822 G.f.: Product_{k>=1} 1/((1 - x^(5*k)) * (1 - x^(5*k - 2)) * (1 - x^(5*k - 3))). - _Vaclav Kotesovec_, Jul 05 2016
%F A036822 a(n) ~ exp(Pi*sqrt(2*n/5)) / (2*sqrt(2*(5+sqrt(5)))*n). - _Vaclav Kotesovec_, Jul 05 2016
%p A036822 c := proc(L,i,n)
%p A036822     local a,p;
%p A036822     a := 0 ;
%p A036822     for p in L do
%p A036822         if modp(p,n) = i then
%p A036822             a := a+1 ;
%p A036822         end if;
%p A036822     end do:
%p A036822     a ;
%p A036822 end proc:
%p A036822 A036822 := proc(n)
%p A036822     local a ,p;
%p A036822     a := 0 ;
%p A036822     for p in combinat[partition](n) do
%p A036822         if c(p,1,5) = 0 then
%p A036822             if c(p,4,5) = 0 then
%p A036822                 a := a+1 ;
%p A036822             end if;
%p A036822         end if;
%p A036822     end do:
%p A036822     a ;
%p A036822 end proc: # _R. J. Mathar_, Oct 19 2014
%t A036822 nmax = 50; Rest[CoefficientList[Series[Product[1/((1 - x^(5*k)) * (1 - x^(5*k-2)) * (1 - x^(5*k-3))), {k, 1, nmax}], {x, 0, nmax}], x]] (* _Vaclav Kotesovec_, Jul 05 2016 *)
%Y A036822 Cf. A036820.
%K A036822 nonn
%O A036822 1,5
%A A036822 _Olivier Gérard_