A394026 - OEIS

A394026

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

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, 12, 13, 13, 20, 17, 18, 18, 21, 22, 24, 27, 29, 29, 33, 33, 36, 36, 42, 41, 49, 51, 55, 55, 58, 60, 66, 70, 78, 81, 87, 89, 97, 99, 106, 109, 121, 124, 134, 141, 154, 157, 167, 172, 186

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,6

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

FORMULA

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).

MATHEMATICA

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 *)

PROG

(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

CROSSREFS

Cf. A241035, A394021, A394027.

Sequence in context: A029298 A262520 A351074 * A383670 A059835 A274659

Adjacent sequences: A394023 A394024 A394025 * A394027 A394028 A394029

KEYWORD

nonn

AUTHOR

Seiichi Manyama, Mar 07 2026

STATUS

approved