A394026 - OEIS

%I #13 Mar 13 2026 22:52:28

%S 0,0,1,1,1,2,0,1,2,1,1,4,2,2,3,3,3,5,3,4,4,6,6,7,6,7,8,9,10,11,10,12,

%T 12,13,13,20,17,18,18,21,22,24,27,29,29,33,33,36,36,42,41,49,51,55,55,

%U 58,60,66,70,78,81,87,89,97,99,106,109,121,124,134,141,154,157,167,172,186

%N Number of partitions p of n with multiplicity of each part at most 2, satisfying max(p) = 2 * min(p).

%H Vincenzo Librandi, <a href="/A394026/b394026.txt">Table of n, a(n) for n = 1..1000</a>

%F G.f.: Sum_{j>=1} q^(3*j)*(1+q^j)*(1+q^(2*j)) * Product_{k=j+1..2*j-1} (1-q^(3*k))/(1-q^k).

%t Nmax=80; a=CoefficientList[Series[Sum[q^(3*j)*(1+q^j)*(1+q^(2*j))*Product[(1-q^(3*k))/(1-q^k),{k,j+1,2*j-1}],{j,1,Nmax}],{q,0,Nmax}],q][[2;;]] (* _Vincenzo Librandi_, Mar 08 2026 *)

%o (Magma) Nmax := 76; R<q> := PowerSeriesRing(Integers(), Nmax+1); S := &+[ q^(3*j)*(1+q^j)*(1+q^(2*j))*(IsEmpty([j+1..2*j-1]) select 1 else &*[(1-q^(3*k))/(1-q^k) : k in [j+1..2*j-1]]) : j in [1..Nmax] ]; a := [Coefficient(S,n) : n in [1..Nmax]]; a; // _Vincenzo Librandi_, Mar 08 2026

%Y Cf. A241035, A394021, A394027.

%K nonn

%O 1,6

%A _Seiichi Manyama_, Mar 07 2026