A394028 - OEIS

A394028

Number of partitions p of n with multiplicity of each part at most 2, satisfying max(p) = 3 * min(p).

0, 0, 0, 1, 1, 1, 2, 3, 2, 2, 2, 3, 2, 3, 3, 6, 4, 6, 7, 10, 10, 10, 10, 15, 14, 17, 17, 21, 20, 22, 24, 32, 29, 34, 37, 41, 45, 50, 54, 64, 64, 74, 76, 88, 95, 104, 111, 128, 130, 141, 153, 169, 179, 199, 212, 235, 244, 266, 282, 313, 330, 361, 383, 423, 447, 483, 515, 561, 589

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OFFSET

1,7

LINKS

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

FORMULA

G.f.: Sum_{j>=1} q^(4*j)*(1+q^j)*(1+q^(3*j)) * Product_{k=j+1..3*j-1} (1-q^(3*k))/(1-q^k).

MATHEMATICA

Nmax=70; Rest@CoefficientList[Series[Sum[q^(4*j)*(1+q^j)*(1+q^(3*j))*Product[(1-q^(3*k))/(1-q^k), {k, j+1, 3*j-1}], {j, 1, Nmax}], {q, 0, Nmax}]//Normal, q] (* Vincenzo Librandi, Mar 09 2026 *)

PROG

(Magma) N := 80; R<q> := PowerSeriesRing(Integers(), N+5); gf := &+[ q^(4*j)*(1+q^j)*(1+q^(3*j))* &*[(1-q^(3*k))/(1-q^k) : k in [j+1..3*j-1]] : j in [1..N] ]; [Coefficient(gf, n) : n in [1..N]]; // Vincenzo Librandi, Mar 09 2026

CROSSREFS

Cf. A241063, A394023, A394029.

Sequence in context: A186181 A324983 A147561 * A210659 A103266 A185150

Adjacent sequences: A394025 A394026 A394027 * A394029 A394030 A394031

KEYWORD

nonn

AUTHOR

Seiichi Manyama, Mar 07 2026

STATUS

approved