A324368 Number of partitions of n that contain {1,2} minus number of partitions of n that contain neither 1 nor 2.

-1, 0, 0, 0, 0, 1, 1, 3, 4, 7, 10, 16, 21, 32, 43, 60, 80, 110, 143, 192, 248, 325, 417, 539, 682, 872, 1097, 1384, 1728, 2163, 2679, 3327, 4097, 5048, 6182, 7570, 9216, 11223, 13599, 16467, 19862, 23940, 28747, 34496, 41260, 49302, 58751, 69938, 83039, 98502, 116572

Offset

0,8

Comments

a(n) > 0 for all n >= 5.

Links

Table of n, a(n) for n=0..50.

Formula

a(n) = A000041(n-2) + A000041(n-1) - A000041(n).

a(n) ~ exp(Pi*sqrt(2*n/3)) / (4*n*sqrt(3)) * (1 - (sqrt(3/2)/Pi + 73*Pi/(24*sqrt(6)))/sqrt(n) + (73/16 + 3025*Pi^2/6912)/n). - Vaclav Kotesovec, Sep 03 2019

G.f.: (q^2+q-1)/Product_{n>=1} (1-q^n). - Shouvik Datta, Sep 07 2019

Mathematica

Table[-(PartitionsP[n] - PartitionsP[n - 1] - PartitionsP[n - 2]), {n, 0, 20}] (* Shouvik Datta, Sep 07 2019 *)

Prog

(PARI) a(n) = numbpart(n-2) + numbpart(n-1) - numbpart(n); \\ Michel Marcus, Sep 03 2019

Crossrefs

Cf. A000041.

Sequence in context: A237833 A275633 A004397 * A241654 A047967 A282893

Adjacent sequences: A324365 A324366 A324367 * A324369 A324370 A324371

Keyword

easy,sign

Author

Max Alekseyev, Sep 03 2019

Status

approved