A394025 Number of partitions p of n into distinct parts such that max(p) = 1 + 3*min(p).

0, 0, 0, 0, 1, 0, 1, 1, 1, 1, 0, 1, 2, 1, 1, 1, 3, 3, 2, 2, 3, 4, 3, 4, 4, 4, 5, 6, 6, 6, 6, 8, 9, 10, 10, 10, 12, 12, 13, 15, 16, 18, 19, 19, 20, 22, 24, 27, 29, 31, 31, 36, 37, 39, 42, 45, 50, 53, 56, 59, 63, 67, 72, 76, 81, 87, 94, 98, 104, 111, 116, 124, 133, 141, 149

Offset

1,13

Links

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

Formula

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

Mathematica

Nmax=60; a=CoefficientList[Series[Sum[q^(4 j+1) Product[1+q^k, {k, j+1, 3 j}], {j, 1, Nmax}], {q, 0, Nmax}], q][[2;; ]] (* Vincenzo Librandi, Mar 07 2026 *)

Prog

(Magma) N := 60; R<q> := PowerSeriesRing(Integers(), N+1); gf := &+[ q^(4*j+1) * &*[1+q^k : k in [j+1..3*j]] : j in [1..N] ]; [Coefficient(gf, n) : n in [1..N]]; // Vincenzo Librandi, Mar 07 2026

Crossrefs

Cf. A241062, A241063, A363075.

Sequence in context: A292745 A047010 A047100 * A124772 A227543 A366920

Adjacent sequences: A394022 A394023 A394024 * A394026 A394027 A394028

Keyword

nonn

Author

Seiichi Manyama, Mar 07 2026

Status

approved